Monoidal Categories And The Gerstenhaber Bracket In Hochschild Cohomology

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Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

Reiner Hermann:
Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology Book PDF

Author : Reiner Hermann:
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 42,5 Mb
Release : 2016-09-06
Category : Associative rings
ISBN : 9781470419950

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Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology by Reiner Hermann: Pdf

In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Lie Theory and Its Applications in Physics

Vladimir Dobrev
Lie Theory and Its Applications in Physics Book PDF

Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 526 pages
File Size : 41,6 Mb
Release : 2023-01-29
Category : Mathematics
ISBN : 9789811947513

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Hochschild Cohomology for Algebras

Sarah J. Witherspoon
Hochschild Cohomology for Algebras Book PDF

Author : Sarah J. Witherspoon
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 52,9 Mb
Release : 2019-12-10
Category : Education
ISBN : 9781470449315

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Hochschild Cohomology for Algebras by Sarah J. Witherspoon Pdf

This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.

Extended Abstracts Spring 2015

Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela
Extended Abstracts Spring 2015 Book PDF

Author : Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela
Publisher : Birkhäuser
Page : 192 pages
File Size : 46,6 Mb
Release : 2016-11-30
Category : Mathematics
ISBN : 9783319454412

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Extended Abstracts Spring 2015 by Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela Pdf

This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.

Homology of Normal Chains and Cohomology of Charges

Th. De Pauw,R. M. Hardt,W. F. Pfeffer
Homology of Normal Chains and Cohomology of Charges Book PDF

Author : Th. De Pauw,R. M. Hardt,W. F. Pfeffer
Publisher : American Mathematical Soc.
Page : 115 pages
File Size : 45,6 Mb
Release : 2017-04-25
Category : Algebraic topology
ISBN : 9781470423353

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Homology of Normal Chains and Cohomology of Charges by Th. De Pauw,R. M. Hardt,W. F. Pfeffer Pdf

The authors consider a category of pairs of compact metric spaces and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary. It includes properly all pairs of compact Lipschitz neighborhood retracts of a large class of Banach spaces. On this category the authors define homology and cohomology functors with real coefficients which satisfy the Eilenberg-Steenrod axioms, but reflect the metric properties of the underlying spaces. As an example they show that the zero-dimensional homology of a space in our category is trivial if and only if the space is path connected by arcs of finite length. The homology and cohomology of a pair are, respectively, locally convex and Banach spaces that are in duality. Ignoring the topological structures, the homology and cohomology extend to all pairs of compact metric spaces. For locally acyclic spaces, the authors establish a natural isomorphism between their cohomology and the Čech cohomology with real coefficients.

Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces

F. Dahmani,V. Guirardel,D. Osin
Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces Book PDF

Author : F. Dahmani,V. Guirardel,D. Osin
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 54,9 Mb
Release : 2017-01-18
Category : Hyperbolic groups
ISBN : 9781470421946

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Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces by F. Dahmani,V. Guirardel,D. Osin Pdf

he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.

Locally Analytic Vectors in Representations of Locally -adic Analytic Groups

Matthew J. Emerton
Locally Analytic Vectors in Representations of Locally adic Analytic Groups Book PDF

Author : Matthew J. Emerton
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 45,9 Mb
Release : 2017-07-13
Category : Geometry, Analytic
ISBN : 9780821875629

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Locally Analytic Vectors in Representations of Locally -adic Analytic Groups by Matthew J. Emerton Pdf

The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.

Proof of the 1-Factorization and Hamilton Decomposition Conjectures

Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Proof of the 1 Factorization and Hamilton Decomposition Conjectures Book PDF

Author : Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 53,5 Mb
Release : 2016-10-05
Category : 1-factorization
ISBN : 9781470420253

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown Pdf

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

The $abc$-Problem for Gabor Systems

Xin-Rong Dai,Qiyu Sun
The abc Problem for Gabor Systems Book PDF

Author : Xin-Rong Dai,Qiyu Sun
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 46,9 Mb
Release : 2016-10-05
Category : Gabor frames
ISBN : 9781470420154

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The $abc$-Problem for Gabor Systems by Xin-Rong Dai,Qiyu Sun Pdf

A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.

Rohlin Flows on von Neumann Algebras

Toshihiko Masuda,Reiji Tomatsu
Rohlin Flows on von Neumann Algebras Book PDF

Author : Toshihiko Masuda,Reiji Tomatsu
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 41,9 Mb
Release : 2016-10-05
Category : Conjugacy classes
ISBN : 9781470420161

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Rohlin Flows on von Neumann Algebras by Toshihiko Masuda,Reiji Tomatsu Pdf

The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III0 factors. Several concrete examples are also studied.

An Inverse Spectral Problem Related to the Geng-Xue Two-Component Peakon Equation

Hans Lundmark,Jacek Szmigielski
An Inverse Spectral Problem Related to the Geng Xue Two Component Peakon Equation Book PDF

Author : Hans Lundmark,Jacek Szmigielski
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 42,9 Mb
Release : 2016-10-05
Category : Discontinuous functions
ISBN : 9781470420260

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An Inverse Spectral Problem Related to the Geng-Xue Two-Component Peakon Equation by Hans Lundmark,Jacek Szmigielski Pdf

The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a ``discrete cubic string'' type-a nonselfadjoint generalization of a classical inhomogeneous string--but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type, implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein's solution of the inverse problem for the Stieltjes string.

Abelian Properties of Anick Spaces

Brayton Gray
Abelian Properties of Anick Spaces Book PDF

Author : Brayton Gray
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 41,7 Mb
Release : 2017-02-20
Category : Abelian groups
ISBN : 9781470423087

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Abelian Properties of Anick Spaces by Brayton Gray Pdf

Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. This work describes their -space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).

Semicrossed Products of Operator Algebras by Semigroups

Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Semicrossed Products of Operator Algebras by Semigroups Book PDF

Author : Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 42,8 Mb
Release : 2017-04-25
Category : Operator algebras
ISBN : 9781470423094

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Semicrossed Products of Operator Algebras by Semigroups by Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis Pdf

The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Intersection Local Times, Loop Soups and Permanental Wick Powers

Yves Le Jan,Michael B. Marcus,Jay Rosen
Intersection Local Times Loop Soups and Permanental Wick Powers Book PDF

Author : Yves Le Jan,Michael B. Marcus,Jay Rosen
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 43,7 Mb
Release : 2017-04-25
Category : Gaussian processes
ISBN : 9781470436957

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Intersection Local Times, Loop Soups and Permanental Wick Powers by Yves Le Jan,Michael B. Marcus,Jay Rosen Pdf

Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

Steve Hofmann,Dorina Mitrea,Marius Mitrea
L p Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets Book PDF

Author : Steve Hofmann,Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 54,9 Mb
Release : 2017-01-18
Category : Function spaces
ISBN : 9781470422608

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$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets by Steve Hofmann,Dorina Mitrea,Marius Mitrea Pdf

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.