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Characters of Groups and Lattices Over Orders : From Ordinary to Integral Representation Theory by Alexander Zimmermann; Walter de Gruyter GmbH & Co. KG is a nonfiction available to read on EtoBox.

What is Characters of Groups and Lattices Over Orders : From Ordinary to Integral Representation Theory about?

Main subject categories: • Group theory • Group rings • Integral representations of finite groups • Representations of orders, lattices, algebras • Class numbersThis is the first textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of finite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the first definitions up to Clifford theory, Brauer's induction theorem and the splitting field theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet's result on primes in arithmetic progressions are given as an application. Examples of integral representations of finite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander-Buchsbaum theorem is proved. The Jordan-Zassenha

Who reads Characters of Groups and Lattices Over Orders : From Ordinary to Integral Representation Theory?

Author

Alexander Zimmermann; Walter de Gruyter GmbH & Co. KG

Publisher

De Gruyter, Walter de Gruyter GmbH

Published

2022

Language

EN

ISBN

9783110702446

Category

nonfiction

Subjects

Mathematics, Symmetry And Group, Stem