Coxeter Bialgebras

Author : Marcelo Aguiar,Swapneel Mahajan
Publisher : Cambridge University Press
Page : 897 pages
File Size : 41,9 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9781009243735

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Coxeter Bialgebras by Marcelo Aguiar,Swapneel Mahajan Pdf

The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.

Author : Marcelo Aguiar,Swapneel Mahajan
Publisher : Cambridge University Press
Page : 853 pages
File Size : 41,5 Mb
Release : 2020-03-19
Category : Mathematics
ISBN : 9781108495806

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Bimonoids for Hyperplane Arrangements by Marcelo Aguiar,Swapneel Mahajan Pdf

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincar -Birkhoff-Witt, and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.

Author : Heinrich G W Begehr,Man-wah Wong,Robert Pertsch Gilbert
Publisher : World Scientific
Page : 1556 pages
File Size : 50,7 Mb
Release : 2003-08-04
Category : Mathematics
ISBN : 9789814485234

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Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) by Heinrich G W Begehr,Man-wah Wong,Robert Pertsch Gilbert Pdf

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.

Author : Heinrich G. W. Begehr,Robert Pertsch Gilbert,Man Wah Wong
Publisher : World Scientific
Page : 1557 pages
File Size : 45,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812385727

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Progress in Analysis by Heinrich G. W. Begehr,Robert Pertsch Gilbert,Man Wah Wong Pdf

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.

Author : Anonim
Publisher : World Scientific
Page : 820 pages
File Size : 49,9 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 8210379456XXX

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by Anonim Pdf

Author : Marcelo Aguiar
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 47,5 Mb
Release : 2006
Category : Education
ISBN : 9780821853542

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Coxeter Groups and Hopf Algebras by Marcelo Aguiar Pdf

An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject.

Author : Jeffrey Bergen,Stefan Catoiu,William Chin
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 50,5 Mb
Release : 2017-04-24
Category : Associative rings and algebras -- Modules, bimodules and ideals -- Modules, bimodules and ideals
ISBN : 9781470428051

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Groups, Rings, Group Rings, and Hopf Algebras by Jeffrey Bergen,Stefan Catoiu,William Chin Pdf

This volume contains the proceedings of the International Conference on Groups, Rings, Group Rings, and Hopf Algebras, held October 2–4, 2015 at Loyola University, Chicago, IL, and the AMS Special Session on Groups, Rings, Group Rings, and Hopf Algebras, held October 3–4, 2015, at Loyola University, Chicago, IL. Both conferences were held in honor of Donald S. Passman's 75th Birthday. Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.

Author : Kevin Broughan
Publisher : Cambridge University Press
Page : 705 pages
File Size : 54,8 Mb
Release : 2023-09-30
Category : Mathematics
ISBN : 9781009384803

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Equivalents of the Riemann Hypothesis by Kevin Broughan Pdf

This third volume presents further equivalents to the Riemann hypothesis and explores its decidability.

Author : Kevin Broughan
Publisher : Cambridge University Press
Page : 706 pages
File Size : 55,5 Mb
Release : 2023-09-30
Category : Mathematics
ISBN : 9781009384773

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Equivalents of the Riemann Hypothesis: Volume 3, Further Steps towards Resolving the Riemann Hypothesis by Kevin Broughan Pdf

This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.

Author : Wolfgang Lay
Publisher : Cambridge University Press
Page : 316 pages
File Size : 44,9 Mb
Release : 2024-05-23
Category : Mathematics
ISBN : 9781009546584

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Higher Special Functions by Wolfgang Lay Pdf

Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.

Author : José Antonio de la Pe?a,Ernesto Vallejo,Natig M. Atakishiyev
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 40,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821836309

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Algebraic Structures and Their Representations by José Antonio de la Pe?a,Ernesto Vallejo,Natig M. Atakishiyev Pdf

The Latin-American conference on algebra, the XV Coloquio Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of plenary sessions of general interest and special sessions on algebraic combinatorics, associative rings, cohomology of rings and algebras, commutative algebra, group representations, Hopf algebras, number theory, quantum groups, and representation theory of algebras. This proceedings volume contains original research papers related to talks at the colloquium. In addition, there are several surveys presenting important topics to a broad mathematical audience. There are also two invited papers by Raymundo Bautista and Roberto Martinez, founders of the Mexican school of representation theory of algebras. The book is suitable for graduate students and researchers interested in algebra.

Author : C. Patrick Bahls
Publisher : World Scientific
Page : 194 pages
File Size : 46,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945540

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The Isomorphism Problem in Coxeter Groups by C. Patrick Bahls Pdf

The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics.The primary purpose of the book is to highlight approximations to the difficult isomorphism problem in Coxeter groups. A number of theorems relating to this problem are stated and proven. Most of the results addressed here concern conditions which can be seen as varying degrees of uniqueness of representations of Coxeter groups. Throughout the investigation, the readers are introduced to a large number of tools in the theory of Coxeter groups, drawn from dozens of recent articles by prominent researchers in geometric and combinatorial group theory, among other fields. As the central problem of the book may in fact be solved soon, the book aims to go further, providing the readers with many techniques that can be used to answer more general questions. The readers are challenged to practice those techniques by solving exercises, a list of which concludes each chapter.

Author : Alexandre V. Borovik,Israel M. Gelfand,Neil White
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220664

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Coxeter Matroids by Alexandre V. Borovik,Israel M. Gelfand,Neil White Pdf

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

Author : Frederick M. Goodman,Pierre de La Harpe,Vaughan F. R. Jones
Publisher : Unknown
Page : 312 pages
File Size : 42,5 Mb
Release : 1989
Category : Class field towers
ISBN : UCAL:B5008739

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Coxeter Graphs and Towers of Algebras by Frederick M. Goodman,Pierre de La Harpe,Vaughan F. R. Jones Pdf

Author : Meinolf Geck,Götz Pfeiffer
Publisher : Oxford University Press
Page : 478 pages
File Size : 41,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0198502508

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Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras by Meinolf Geck,Götz Pfeiffer Pdf

Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.