Lectures on Block Theory
Block theory is a part of the theory of modular representation of finite groups and deals with the algebraic structure of blocks. In this volume Burkhard Külshammer starts with the classical structure theory of finite dimensional algebras, and leads up to Puigs main result on the structure of the so called nilpotent blocks, which he discusses in the final chapter. All the proofs in the text are given clearly and in full detail, and suggestions for further reading are also included. For researchers and graduate students interested in group theory or representation theory, this book will form an excellent self contained introduction to the theory of blocks.
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Simple and Semisimple Algebras
Points and Maximal Ideals
Miscellaneous Results on Algebras
Groups Acting on Algebras
Groups in Algebras
A-submodules abstract algebras algebra over F algebraically closed field called classes of G conjugacy classes defect groups defect pointed subgroup denote direct embedding embedding of interior epimorphism FCG(P FG with nilpotent finite group follows easily form a basis FP-module Frobenius formula G on FG group algebra Hence homomorphism of algebras homomorphism of interior iFGi implies interior G-algebra isomorphic to Mat(n isomorphism of algebras isomorphism of interior K C H kernel Krull-Schmidt theorem Let F let H let P7 local algebra Mat(n,F maximal ideal maximal local pointed modules Moreover nilpotent blocks nilpotent ideal non-zero idempotent orthogonal primitive idempotents p-group p-subgroup p'-section pairwise orthogonal primitive particular point of G pointed group positive integer prime characteristic projective left A-module Proof proper subgroup RCG(Q result is proved satisfying simple algebra subgroup H subgroup of Hp suffices to show symmetric algebra theory unique point unitary subalgebra
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