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# π Frobenius Algebras: No. II: Tilted and Hochschild Extension Algebras by Andrzej Skowronski, Kunio Yamagata β 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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This volume is based on the author's lecture courses to algebraists at Munich and at Goteborg. He presents, for the first time in book form, a unified approach from the point of view of Frobenius algebras/extensions to diverse topics, such as Jones' subfa...

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 monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms....

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 ...

The final part of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers ...

Volume II completes the description of the main aspects of the theory, covering representation questions, model theory and decision problems for them, translations from logic to algebra and vice-versa, and relationships with other algebraic versions of lo...

The final part of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers ...

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms....