By C. B. Thomas
The aim of this ebook is to check the relation among the illustration ring of a finite workforce and its critical cohomology through attribute periods. during this manner it truly is attainable to increase the identified calculations and end up a few common effects for the imperative cohomology ring of a bunch G of top strength order. one of the teams thought of are these of p-rank lower than three, extra-special p-groups, symmetric teams and linear teams over finite fields. a major device is the Riemann - Roch formulation which gives a relation among the attribute sessions of an caused illustration, the sessions of the underlying illustration and people of the permutation illustration of the endless symmetric crew. Dr Thomas additionally discusses the results of his paintings for a few mathematics teams in an effort to curiosity algebraic quantity theorists. Dr Thomas assumes the reader has taken uncomplicated classes in algebraic topology, staff idea and homological algebra, yet has incorporated an appendix within which he offers a merely topological facts of the Riemann - Roch formulation.
Read or Download Characteristic Classes and the Cohomology of Finite Groups (Cambridge Studies in Advanced Mathematics) PDF
Best 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 noticeable: functions to random quadratic types (sums of squares), the research of algebraic simplifications of maxi mum chance estimation of patterned covariance matrices, and a extra broad 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 objective of those lectures is to introduce a newbie to the finite dimensional representations of Lie teams and Lie algebras. due to the fact this objective is shared via a variety of different books, we must always clarify during this Preface how our strategy differs, even though the aptitude reader can most likely see this greater by means of a brief flick thru the publication.
"A remarkably intelligible survey . . . good geared up, good written and intensely transparent all through. " — Mathematical ReviewsThis first-class textual content, lengthy one in every of the best-written, so much skillful expositions of staff conception and its actual purposes, is directed essentially to complex undergraduate and graduate scholars in physics, in particular quantum physics.
Extra resources for Characteristic Classes and the Cohomology of Finite Groups (Cambridge Studies in Advanced Mathematics)