By Mara D. Neusel

ISBN-10: 0821829165

ISBN-13: 9780821829165

The questions which have been on the middle of invariant thought because the nineteenth century have revolved round the following topics: finiteness, computation, and specified sessions of invariants. This ebook 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 aspect and current the recognized solutions, open difficulties, and techniques 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 provides distinct sessions of invariants, which take care of modular invariant conception and its specific difficulties and lines. bankruptcy 7 collects effects for specified sessions 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 latest instruments. this kind of is the Steenrod algebra, which the authors introduce in bankruptcy eight to unravel the inverse invariant conception challenge, round which the authors have geared up the final 3 chapters. The ebook includes quite a few examples to demonstrate the speculation, frequently of greater than passing curiosity, and an appendix on commutative graded algebra, which supplies a few of the required easy historical past. there's an intensive reference checklist to supply the reader with orientation to the enormous literature.

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