The Homology of Special Linear Groups Over Laurent Polynomial Rings
Author : Kevin Patrick Knudson
Publisher :
Page : 144 pages
File Size : 28,96 MB
Release : 1996
Category : Homology theory
ISBN :
Author : Kevin Patrick Knudson
Publisher :
Page : 144 pages
File Size : 28,96 MB
Release : 1996
Category : Homology theory
ISBN :
Author : Surender K. Gupta
Publisher :
Page : 113 pages
File Size : 40,39 MB
Release : 1980
Category : Algebraic fields
ISBN : 9780333903636
Author : Bertram Wehrfritz
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 20,54 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642870813
By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.
Author : Vincent Franjou
Publisher : Birkhäuser
Page : 154 pages
File Size : 18,89 MB
Release : 2015-12-08
Category : Mathematics
ISBN : 3319213059
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.
Author :
Publisher :
Page : 756 pages
File Size : 26,46 MB
Release : 2002
Category : Dissertations, Academic
ISBN :
Author : Walter Borho
Publisher : Springer Science & Business Media
Page : 141 pages
File Size : 14,61 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461245583
1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.
Author : Stefan Witzel
Publisher :
Page : 0 pages
File Size : 44,22 MB
Release : 2011
Category :
ISBN :
Author : John D. Dixon
Publisher : London ; Toronto : Van Nostrand Reinhold Company
Page : 196 pages
File Size : 44,66 MB
Release : 1971
Category : Mathematics
ISBN :
Author : American Mathematical Society
Publisher :
Page : 718 pages
File Size : 27,10 MB
Release : 2005
Category : Mathematics
ISBN :
Author : Warren Dicks
Publisher : Cambridge University Press
Page : 304 pages
File Size : 26,44 MB
Release : 1989-03-09
Category : Mathematics
ISBN : 9780521230339
Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.