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Representations of Algebras - Tame and Wild Behavior (Hardcover, 1st ed. 2022)
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Representations of Algebras - Tame and Wild Behavior (Hardcover, 1st ed. 2022)
Series: Algebra and Applications, 30
Expected to ship within 12 - 17 working days
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This book offers an original introduction to the representation
theory of algebras, suitable for beginning researchers in algebra.
It includes many results and techniques not usually covered in
introductory books, some of which appear here for the first time in
book form. The exposition employs methods from linear algebra
(spectral methods and quadratic forms), as well as categorical and
homological methods (module categories, Galois coverings,
Hochschild cohomology) to present classical aspects of ring theory
under new light. This includes topics such as rings with several
objects, the Harada-Sai lemma, chain conditions, and
Auslander-Reiten theory. Noteworthy and significant results covered
in the book include the Brauer-Thrall conjectures, Drozd's theorem,
and criteria to distinguish tame from wild algebras. This text may
serve as the basis for a second graduate course in algebra or as an
introduction to research in the field of representation theory of
algebras. The originality of the exposition and the wealth of
topics covered also make it a valuable resource for more
established researchers.
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