Representations and Cohomology: Volume 2, Cohomology of Groups and Modules (Cambridge Studies in Advanced Mathematics, Series Number 31) - Hardcover
Book 14 of 140: Cambridge Studies in Advanced Mathematics
Synopsis
This is the second of two volumes which will provide an introduction to modern developments in the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of representations of finite dimensional algebras; the author emphasises modular representations and the homological algebra associated with their categories. This volume concentrates on the cohomology of groups, always with representations in view, however. It begins with a background reference chapter, then proceeds to an overview of the algebraic topology and K-theory associated with cohomology of groups, especially the work of Quillen. Later chapters look at algebraic and topological proofs of the finite generation of the cohomology ring of a finite group, and an algebraic approach to the Steenrod operations in group cohomology. The book cumulates in a chapter dealing with the theory of varieties for modules. Much of the material presented here has never appeared before in book form. Consequently students and research workers studying group theory, and indeed algebra in general, will be grateful to Dr Benson for supplying an exposition of a good deal of the essential results of modern representation theory.
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Review
."..will certainly have a considerable influence on the further development of the subject." B. K^D"ulshammer, Zentralblatt f^D"ur Mathematik und ihre Grenzgebiete "It will surely give the research area of 'group cohomology' new impetus. It contains most of the results known about cohomology of groups, much of which had previously only been available in research papers." K.W. Roggenkamp, Mathematical Reviews "Benson's exposition is locally clear and engaging...his books are ideally suited for a graduate student or practicing group theorist who wants to reach the current research frontier rapidly. All in all, Benson has done an admirable job of drawing together the most important current ideas relating group representations to topology and group cohomology." J.E. Humphreys, Bulletin of the American Mathematical Society
Book Description
This is the second of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras. Much of the material presented here has never appeared before in book form.
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REPRESENTATIONS AND COHOMOLOGY, II : COHOMOLOGY OF GROUPS AND MODULES
Published by
Cambridge University Press, Cambridge, 1991
ISBN 10: 0521361354
ISBN 13: 9780521361354
Used
Hardcover
Seller: Aardvark Rare Books, EUGENE, OR, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: VERY GOOD PLUS. Very mild edgewear to boards with the exception of a .625" dent to front board near fore-edge. Spinecaps very gently folded under. A faint 1.5" curved mark to lower fore-edge. White and red lettering to spine and front of pewter colored boards. A 6 x 1", red diagonal bar, edged in white with a black line down the center, to lower right portion of front cover. Numerous illustrations. Clean, tight, bright. 278 pp. with bibliography and index. Cambridge studies in advanced mathematics 31. This is the second of two volumes which have grown out of about seven years of graduate courses on various aspects of representation theory and cohomology of groups, given at Yale, Northwestern and Oxford. Contents include : Background material from algebraic topology, Cohomology of groups, Spectral sequences, The Evens norm map and the Steenrod algebra, Varieties for modules and multiple complexes, Group actions and the Steinberg module and Local coefficients on subgroup complexes. Chapter 5, in a sense, "is the central chapter of the entire two volumes, since it shows how inextricably intertwined representation theory and cohomology really are," (introduction). Seller Inventory # 69824