The block theory of finite group algebras. [E-Book] / Markus Linckelmann. Volume II
Linckelmann, Markus, (author)
Cambridge : Cambridge University Press, 2018
1 online resource (xi, 510 pages)
englisch
9781108425902
9781108441803
9781108349307
London Mathematical Society student texts ; 92
Full Text
This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.