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# đź“™ Frobenius Algebras: No. II: Tilted and Hochschild Extension Algebras by Andrzej Skowronski, Kunio Yamagata â€” pdf free

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This is the second of three volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book is devoted to fundamental results of the representation theory of finite dimensional hereditary algebras and their tilted algebras, which allow to describe the representation theory of prominent classes of Frobenius algebras.
The second part is devoted to basic classical and recent results concerning the Hochschild extensions of finite dimensional algebras by duality bimodules and their module categories. Moreover, the shapes of connected components of the stable Auslander-Reiten quivers of Frobenius algebras are described.
The only prerequisite in this volume is a basic knowledge of linear algebra and some results of the first volume. It includes complete proofs of all results presented and provides a rich supply of examples and exercises.
The text is primarily addressed to graduate students starting research in the representation theory of algebras as well mathematicians working in other fields.
Keywords: Algebra, module, bimodule, representation, quiver, ideal, radical, simple module, semisimple module, uniserial module, projective module, injective module, tilting module, hereditary algebra, tilted algebra, Frobenius algebra, symmetric algebra, selfinjective algebra, Hochschild extension algebra, category, functor, torsion pair, projective dimension, injective dimension, global dimension, Euler form, Grothendieck group, irreducible homomorphism, almost split sequence, Auslander-Reiten translation, Auslander-Reiten quiver, stable equivalence, syzygy module, duality bimodule, Hochschild extension

## About book:

## About file:

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- Series:
**EMS Textbooks in Mathematics** - Author:
**Andrzej Skowronski, Kunio Yamagata** - Year:
**2017** - Publisher:
**European Mathematical Society** - Language:
**English** - ISBN:
**3037191740,9783037191743**

- File size:
**4 161 208** - Format:
**pdf**

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Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years representation theory has been an area of intense research and the author shows that derived categories of...

Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years representation theory has been an area of intense research and the author shows that derived categories of...

This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book can be recommended either as a textbook for ...

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory ...

Content: Preface.- Bibliograph.- Curriculum Vitae.- Comments by Bertram Kostant on Papers in Volume I.- Holonomy and the Lie Algebra of Infinitesimal Motions of a Riemannian Manifold, 1955.- On the Conjugacy of Real Cartan Subalgebras I, 1995.- On the Con...

Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991.After finishing high school in his home town, he studied at the Jagiellonian University in KrakĂłw. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In...

The causes, events and legacy of World War II are the subjects of this 2-vol. set. Part of the UÂ·XÂ·LR World War II Reference Library, World War II: Almanac provides extensive background information and includes contrary viewpoints that are presented in an...

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First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation t...

In this book, Michael Slater provides a new assessment of pragmatist views in the philosophy of religion. Focusing on the tension between naturalist and anti-naturalist versions of pragmatism, he argues that the anti-naturalist religious views of philosop...

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The story of the Palestinian people...

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