Derived Functors And B Cohomology On Quantum Groups

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Derived Functors And B Cohomology On Quantum Groups

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Author : Marie Engelbrecht Hougaard
language : en
Publisher:
Release Date : 2009

Derived Functors And B Cohomology On Quantum Groups written by Marie Engelbrecht Hougaard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.

Derived Functors And Sheaf Cohomology

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Author : Ugo Bruzzo
language : en
Publisher: World Scientific
Release Date : 2020-03-10

Derived Functors And Sheaf Cohomology written by Ugo Bruzzo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.

The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.

Cohomology For Quantum Groups Via The Geometry Of The Nullcone

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Author : Christopher P. Bendel
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-07

Cohomology For Quantum Groups Via The Geometry Of The Nullcone written by Christopher P. Bendel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-07 with Mathematics categories.

In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.

Topics In Cohomology Of Groups

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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-08-19

Topics In Cohomology Of Groups written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-19 with Mathematics categories.

The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.

Quantum Groups Noncommutative Geometry And Fundamental Physical Interactions

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Author : Daniel Kastler
language : en
Publisher:
Release Date : 1999

Quantum Groups Noncommutative Geometry And Fundamental Physical Interactions written by Daniel Kastler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Contents include: Hochschild Homology of Function Algebras Associated with Singularities; On the KK-Theory of Stable Projective Limits; Noncommutative Integrability; Gauge Invariance of the Chern-Simons Action in Noncommutative Geometry; The Analysis of the Hochshild Homology; Coproducts and Operations on Cyclic Cohomology; Powers of Quantum Matrices and Relations Between Them; Introductory Notes on Extensions of Hopf Algebras; Hopf Algebras from the Quantum Geometry Point of View; Equation Pentagonale, Bige bres et Espaces de Modules; Chiral Anomalies in the Spectral Action; Standard Model and Unimodularity Condition; On Feynman Graphs as Elements of a Hopf Algebra.

Quantum Groups And Noncommutative Spaces

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Author : Matilde Marcolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-02

Quantum Groups And Noncommutative Spaces written by Matilde Marcolli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-02 with Mathematics categories.

This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.

Quantum Linear Groups

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Author : Brian Parshall
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Quantum Linear Groups written by Brian Parshall and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

We consider the theory of quantum groups as a natural abstraction of the theory of affine group schemes. After establishing the foundational results as the theory of induced representations, rational cohomology, and the Hochschild-Serre spectral sequence, we take up a detailed investigation of the quantum linear group [italic]GL[italic subscript]q([italic]n). In particular, we develop the global and infinitesimal representation theory of [italic]GL[italic subscript]q([italic]n) and its subgroups.

Cohomology As The Derived Functor Of Derivations

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Author : George S. Rinehart
language : en
Publisher:
Release Date : 1963*

Cohomology As The Derived Functor Of Derivations written by George S. Rinehart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963* with categories.

Hopf Algebras And Quantum Groups

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Author : Stefaan Caenepeel
language : en
Publisher: CRC Press
Release Date : 2019-05-07

Hopf Algebras And Quantum Groups written by Stefaan Caenepeel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.

This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum g

Lectures On Functor Homology

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Author : Vincent Franjou
language : en
Publisher:
Release Date : 2015

Lectures On Functor Homology written by Vincent Franjou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament's theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko's unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert's fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin's strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov's lectures highlight topological invariants: homotopy and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touzé's introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.