Group Theory

Download E-books Invariant Theory of Finite Groups (Mathematical Surveys and Monographs) PDF

By Mara D. Neusel

The questions which have been on the heart of invariant thought because the nineteenth century have revolved round the following topics: finiteness, computation, and distinctive periods of invariants. This publication starts with a survey of many concrete examples selected from those topics within the algebraic, homological, and combinatorial context. In extra chapters, the authors choose one or the opposite of those questions as a departure element and current the recognized solutions, open difficulties, and strategies and instruments had to receive those solutions. bankruptcy 2 offers with algebraic finiteness. bankruptcy three offers with combinatorial finiteness. bankruptcy four offers Noetherian finiteness. bankruptcy five addresses homological finiteness. bankruptcy 6 offers precise periods of invariants, which take care of modular invariant idea and its specific difficulties and lines. bankruptcy 7 collects effects for distinctive periods of invariants and coinvariants equivalent to (pseudo) mirrored image teams and representations of low measure. If the floor box is finite, extra difficulties look and are compensated for partially by means of the emergence of recent instruments. this type of is the Steenrod algebra, which the authors introduce in bankruptcy eight to unravel the inverse invariant conception challenge, round which the authors have prepared the final 3 chapters. The booklet comprises various examples to demonstrate the idea, frequently of greater than passing curiosity, and an appendix on commutative graded algebra, which supplies the various required simple historical past. there's an intensive reference checklist to supply the reader with orientation to the huge literature.

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