Hopf Algebras in General and in Combinatorial Physics: a practical introduction
by G.H.E. Duchamp, et al.
Publisher: arXiv 2008
Number of pages: 40
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced.
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by E.B. Elliott - The Clarendon Press
The primary object of this book is that of explaining with all the clearness at my command the leading principles of invariant algebra, in the hope of making it evident to the junior student that the subject is attractive as well as important.
by W. B. Vasantha Kandasamy, Florentin Smarandache - Educational Publisher
This book brings out how sets in algebraic structures can be used to construct the most generalized algebraic structures, like set linear algebra / vector space, set ideals in groups and rings and semigroups, and topological set vector spaces.
by W. B. Vasantha Kandasamy - American Research Press
Near-rings are one of the generalized structures of rings. This is a book on Smarandache near-rings where the Smarandache analogues of the near-ring concepts are developed. The reader is expected to have a background in algebra and in near-rings.
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From the table of contents: Morita equivalence (Hom, Bimodules, Projective modules ...); Localization and Goldie's theorem; Central simple algebras and the Brauer group; Maximal orders; Irreducible representations; Growth of algebras.