Representations of algebras : tame and wild behavior / José Antonio de la Peña.
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 meth...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Cham :
Springer,
[2022]
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| Series: | Algebras and applications ;
v. 30. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | 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 HaradaSai lemma, chain conditions, and AuslanderReiten theory. Noteworthy and significant results covered in the book include the BrauerThrall conjectures, Drozds 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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| Physical Description: | 1 online resource (xiv, 233 pages) : illustrations. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 3031122879 9783031122873 3031122887 9783031122880 |