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Author : I-Chiau Huang
Publisher : Unknown
Page : 53 pages
File Size : 44,6 Mb
Release : 1995
Category : Injective modules
ISBN : 1470401274
Author : I-Chiau Huang
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 55,5 Mb
Release : 1995
Category : Injective modules
ISBN : 9780821826089
Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.
Author : Paul S. Muhly,Baruch Solel
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 45,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803462
This book gives a general systematic analysis of the notions of ``projectivity'' and ``injectivity'' in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra $A$ is simply the Hilbert space of a (contractive) representation of $A$ viewed as a module over $A$ in the usual way. In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras. The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a ``tree'' in the sense of computer directories.
Author : Valentina Barucci,David E. Dobbs,Marco Fontana
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 54,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805442
If $k$ is a field, $T$ an analytic indeterminate over $k$, and $n_1, \ldots, n_h$ are natural numbers, then the semigroup ring $A = k[[T^{n_1}, \ldots, T^{n_h}]]$ is a Noetherian local one-dimensional domain whose integral closure, $k[[T]]$, is a finitely generated $A$-module. There is clearly a close connection between $A$ and the numerical semigroup generated by $n_1, \ldots, n_h$. More generally, let $A$ be a Noetherian local domain which is analytically irreducible and one-dimensional (equivalently, whose integral closure $V$ is a DVR and a finitely generated $A$-module). As noted by Kunz in 1970, some algebraic properties of $A$ such as ``Gorenstein'' can be characterized by using the numerical semigroup of $A$ (i.e., the subset of $N$ consisting of all the images of nonzero elements of $A$ under the valuation associated to $V$ ). This book's main purpose is to deepen the semigroup-theoretic approach in studying rings A of the above kind, thereby enlarging the class of applications well beyond semigroup rings. For this reason, Chapter I is devoted to introducing several new semigroup-theoretic properties which are analogous to various classical ring-theoretic concepts. Then, in Chapter II, the earlier material is applied in systematically studying rings $A$ of the above type. As the authors examine the connections between semigroup-theoretic properties and the correspondingly named ring-theoretic properties, there are some perfect characterizations (symmetric $\Leftrightarrow$ Gorenstein; pseudo-symmetric $\Leftrightarrow$ Kunz, a new class of domains of Cohen-Macaulay type 2). However, some of the semigroup properties (such as ``Arf'' and ``maximal embedding dimension'') do not, by themselves, characterize the corresponding ring properties. To forge such characterizations, one also needs to compare the semigroup- and ring-theoretic notions of ``type''. For this reason, the book introduces and extensively uses ``type sequences'' in both the semigroup and the ring contexts.
Author : Joseph Lipman,Suresh Nayak,Pramathanath Sastry
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 46,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837054
Robert Hartshorne's 1966 book, Residues and Duality, introduced the notion of residual complexes and developed a duality theory (Grothendieck duality) on the category of maps of noetherian schemes. The three articles in this volume constitute a reworking of the main parts of the corresponding chapters in Hartshorne's 1966 book in greater generality using a somewhat different approach. Additionally, the authors' motivation is to help readers gain a better understanding of the relation between local properties of residues and global properties of the dualizing pseudofunctor. The book is suitable for graduate students and researchers working in algebraic geometry.
Author : Paul Kirk,Eric Klassen
Publisher : American Mathematical Soc.
Page : 58 pages
File Size : 47,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805381
The subject of this memoir is the spectrum of a Dirac-type operator on an odd-dimensional manifold M with boundary and, particularly, how this spectrum varies under an analytic perturbation of the operator. Two types of eigenfunctions are considered: first, those satisfying the ``global boundary conditions'' of Atiyah, Patodi, and Singer and second, those which extend to $L^2$ eigenfunctions on M with an infinite collar attached to its boundary. The unifying idea behind the analysis of these two types of spectra is the notion of certain ``eigenvalue-Lagrangians'' in the symplectic space $L^2(\partial M)$, an idea due to Mrowka and Nicolaescu. By studying the dynamics of these Lagrangians, the authors are able to establish that those portions of the two types of spectra which pass through zero behave in essentially the same way (to first non-vanishing order). In certain cases, this leads to topological algorithms for computing spectral flow.
Author : Ajit Iqbal Singh
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 44,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805398
It is now well known that the measure algebra $M(G)$ of a locally compact group can be regarded as a subalgebra of the operator algebra $B(B(L^2(G)))$ of the operator algebra $B(L^2(G))$ of the Hilbert space $L^2(G)$. In this memoir, the author studies the situation in hypergroups and finds that, in general, the analogous map for them is neither an isometry nor a homomorphism. However, it is completely positive and completely bounded in certain ways. This work presents the related general theory and special examples.
Author : Edward Cline,Brian Parshall,Leonard Scott,Leonard L. Scott
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 46,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804889
Suppose that $R$ is a finite dimensional algebra and $T$ is a right $R$-module. Let $A = \mathrm{ End}_R(T)$ be the endomorphism algebra of $T$. This memoir presents a systematic study of the relationships between the representation theories of $R$ and $A$, especially those involving actual or potential structures on $A$ which ''stratify'' its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups. The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ''Specht/Weyl module'' correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.
Author : Friedrich Tomi,Anthony Tromba
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 45,6 Mb
Release : 1995
Category : Index theorems
ISBN : 9780821803523
In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
Author : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 49 pages
File Size : 52,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804056
Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.
Author : Jane Gilman
Publisher : American Mathematical Soc.
Page : 221 pages
File Size : 41,6 Mb
Release : 1995
Category : Fuchsian groups
ISBN : 9780821803615
The discreteness problem is the problem of determining whether or not a two-generator subgroup of $PSL(2, R)$ is discrete. Historically, papers on this old and subtle problem have been known for their errors and omissions. This book presents the first complete geometric solution to the discreteness problem by building upon cases previously presented by Gilman and Maskit and by developing a theory of triangle group shinglings/tilings of the hyperbolic plane and a theory explaining why the solution must take the form of an algorithm. This work is a thoroughly readable exposition that captures the beauty of the interplay between the algebra and the geometry of the solution.
Author : Chris Jantzen
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 45,7 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 9780821804827
This memoir studies reducibility in a certain class of induced representations for and , where is -adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.
Author : Hans J. Baues
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 54,6 Mb
Release : 1980
Category : Mathematics
ISBN : 9780821822302
Author : Samuel Kaplan
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 44,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804636
This book, based on the author's monograph, ``The Bidual of C(X) I'', throws new light on the subject of Lebesgue integration and contributes to clarification of the structure of the bidual of C(X). Kaplan generalizes to the bidual the theory of Lebesgue integration, with respect to Radon measures on X, of bounded functions (X is assumed to be compact). The bidual of C(X) contains this space of bounded functions, but is much more ``spacious'', so the body of results can be expected to be richer. Finally, the author shows that by projection onto the space of bounded functions, the standard theory is obtained.
Author : H. Andréka,Steven R. Givant,I. Németi
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 43,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805954
This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.
