Dualities on Generalized Koszul Algebras
Dualities on Generalized Koszul Algebras

Author: Edward L. Green

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 90

ISBN-13: 0821829343

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Koszul rings are graded rings which have played an important role in algebraic topology, noncommutative algebraic geometry and in the theory of quantum groups. One aspect of the theory is to compare the module theory for a Koszul ring and its Koszul dual. There are dualities between subcategories of graded modules; the Koszul modules.

Relative Nonhomogeneous Koszul Duality
Relative Nonhomogeneous Koszul Duality

Author: Leonid Positselski

Publisher: Springer Nature

Published: 2022-02-10

Total Pages: 303

ISBN-13: 3030895408

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This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare–Birkhoff–Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.

Algebras and Modules II
Algebras and Modules II

Author: Idun Reiten

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 596

ISBN-13: 9780821810767

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The 43 research papers demonstrate the application of recent developments in the representation theory of artin algebras and related topics. Among the algebras considered are tame, bi- serial, cellular, factorial hereditary, Hopf, Koszul, non- polynomial growth, pre-projective, Termperley-Lieb, tilted, and quasi-tilted. Other topics include tilting and co-tilting modules and generalizations as *-modules, exceptional sequences of modules and vector bundles, homological conjectives, and vector space categories. The treatment assumes knowledge of non- commutative algebra, including rings, modules, and homological algebra at a graduate or professional level. No index. Member prices are $79 for institutions and $59 for individuals, which also apply to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR

New Spaces in Mathematics: Volume 1
New Spaces in Mathematics: Volume 1

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04-01

Total Pages: 602

ISBN-13: 1108848214

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After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.

Trends in the Representation Theory of Finite Dimensional Algebras
Trends in the Representation Theory of Finite Dimensional Algebras

Author: Edward L. Green

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 378

ISBN-13: 0821809288

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This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory.

The Connective K-Theory of Finite Groups
The Connective K-Theory of Finite Groups

Author: Robert Ray Bruner

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 144

ISBN-13: 0821833669

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Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group

Interpolation of Weighted Banach Lattices/A Characterization of Relatively Decomposable Banach Lattices
Interpolation of Weighted Banach Lattices/A Characterization of Relatively Decomposable Banach Lattices

Author: Michael Cwikel

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 142

ISBN-13: 0821833820

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Includes a paper that provides necessary and sufficient conditions on a couple of Banach lattices of measurable functions $(X_{0}, X_{1})$ which ensure that, for all weight functions $w_{0}$ and $w_{1}$, the couple of weighted lattices $(X_{0, w_{0}}, X_{1, w_{1}})$ is a Calderon-Mityagin cou

Extending Intersection Homology Type Invariants to Non-Witt Spaces
Extending Intersection Homology Type Invariants to Non-Witt Spaces

Author: Markus Banagl

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 101

ISBN-13: 0821829882

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Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces.

Radially Symmetric Patterns of Reaction-Diffusion Systems
Radially Symmetric Patterns of Reaction-Diffusion Systems

Author: Arnd Scheel

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 102

ISBN-13: 0821833731

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Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.

Invariants of Boundary Link Cobordism
Invariants of Boundary Link Cobordism

Author: Desmond Sheiham

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 128

ISBN-13: 0821833405

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An $n$-dimensional $\mu$-component boundary link is a codimension $2$ embedding of spheres $L=\sqcup_{\mu}S DEGREESn \subset S DEGREES{n+2}$ such that there exist $\mu$ disjoint oriented embedded $(n+1)$-manifolds which span the components of $L$. This title proceeds to compute the isomorphism class of $C_{