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.
Read or Download Invariant Theory of Finite Groups (Mathematical Surveys and Monographs) PDF
Similar Group Theory books
This monograph brings jointly my paintings in mathematical facts as i've got seen it in the course of the lens of Jordan algebras. 3 technical domain names are to be visible: functions to random quadratic varieties (sums of squares), the research of algebraic simplifications of maxi mum chance estimation of patterned covariance matrices, and a extra huge open mathematical exploration of the algebraic area from which i've got drawn the implications utilized in the statistical difficulties simply pointed out.
The first target of those lectures is to introduce a newbie to the finite dimensional representations of Lie teams and Lie algebras. due to the fact that this aim is shared through various different books, we should always clarify during this Preface how our strategy differs, even supposing the capability reader can most likely see this greater via a short flick thru the publication.
"A remarkably intelligible survey . . . good geared up, good written and intensely transparent all through. " — Mathematical ReviewsThis very good textual content, lengthy certainly one of the best-written, such a lot skillful expositions of crew conception and its actual purposes, is directed essentially to complicated undergraduate and graduate scholars in physics, specially quantum physics.
Additional info for Invariant Theory of Finite Groups (Mathematical Surveys and Monographs)