Rational Representations The Steenrod Algebra And Functor Homology
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Rational Representations The Steenrod Algebra And Functor Homology
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Author : Vincent Franjou
language : en
Publisher:
Release Date : 2003
Rational Representations The Steenrod Algebra And 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 2003 with Mathematics categories.
The book presents aspects of homological algebra in functor categories, with emphasis on polynomial functors between vector spaces over a finite field. With these foundations in place, the book presents applications to representation theory, algebraic topology and $K$-theory. As these applications reveal, functor categories offer powerful computational techniques and theoretical insights. T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander then presents applications to the rational representations of general linear groups. L. Schwartz emphasizes the relation of functor categories to the Steenrod algebra. Finally, V. Franjou and T. Pirashvili present A. Scorichenko's understanding of the stable $K$-theory of rings as functor homology. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.
Lectures On Functor Homology
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Author : Vincent Franjou
language : en
Publisher: Birkhäuser
Release Date : 2015-12-08
Lectures On Functor Homology written by Vincent Franjou and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics 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: homoto py 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.
Geometric And Topological Aspects Of The Representation Theory Of Finite Groups
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Author : Jon F. Carlson
language : en
Publisher: Springer
Release Date : 2018-10-04
Geometric And Topological Aspects Of The Representation Theory Of Finite Groups written by Jon F. Carlson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Mathematics categories.
These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
An Alpine Expedition Through Algebraic Topology
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Author : Christian Ausoni
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-09
An Alpine Expedition Through Algebraic Topology written by Christian Ausoni 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 2014-06-09 with Mathematics categories.
This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.
Algebraic Topology
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Author : Jaume Aguade
language : en
Publisher: Springer
Release Date : 2006-11-15
Algebraic Topology written by Jaume Aguade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The papers in this collection, all fully refereed, original papers, reflect many aspects of recent significant advances in homotopy theory and group cohomology. From the Contents: A. Adem: On the geometry and cohomology of finite simple groups.- D.J. Benson: Resolutions and Poincar duality for finite groups.- C. Broto and S. Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C. Ravenel: Morava K-theories of classifying spaces and generalized characters for finite groups.- K. Ishiguro: Classifying spaces of compact simple lie groups and p-tori.- A.T. Lundell: Concise tables of James numbers and some homotopyof classical Lie groups and associated homogeneous spaces.- J.R. Martino: Anexample of a stable splitting: the classifying space of the 4-dim unipotent group.- J.E. McClure, L. Smith: On the homotopy uniqueness of BU(2) at the prime 2.- G. Mislin: Cohomologically central elements and fusion in groups.
From Categories To Homotopy Theory
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Author : Birgit Richter
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-16
From Categories To Homotopy Theory written by Birgit Richter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-16 with Mathematics categories.
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Advances In Combinatorial Mathematics
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Author : Ilias S. Kotsireas
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-06
Advances In Combinatorial Mathematics written by Ilias S. Kotsireas 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 2009-11-06 with Mathematics categories.
The Second Waterloo Workshop on Computer Algebra was dedicated to the 70th birthday of combinatorics pioneer Georgy Egorychev. This book of formally-refereed papers submitted after that workshop covers topics closely related to Egorychev’s influential works.
Rational Representations Of Algebraic Groups
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Author : Stephen Donkin
language : en
Publisher: Springer
Release Date : 2006-11-14
Rational Representations Of Algebraic Groups written by Stephen Donkin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Rational Homotopy Theory
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Author : Yves Felix
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Rational Homotopy Theory written by Yves Felix 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 2001 with Mathematics categories.
This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.
Group Representation Theory
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Author : Meinolf Geck
language : en
Publisher: EPFL Press
Release Date : 2007-05-07
Group Representation Theory written by Meinolf Geck and has been published by EPFL Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-07 with Mathematics categories.
After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).