# Frobenius Algebras I: Basic Representation Theory

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*Andrzej Skowroński; Kunio Yamagata*

A publication of the European Mathematical Society

This is the first of two volumes which will provide a comprehensive
introduction to the modern representation theory of Frobenius algebras. The
first part of the book serves as a general introduction to basic results and
techniques of the modern representation theory of finite dimensional
associative algebras over fields, including the Morita theory of equivalences
and dualities and the Auslander–Reiten theory of irreducible morphisms and
almost split sequences.

The second part is devoted to fundamental classical and recent results
concerning the Frobenius algebras and their module categories. Moreover, the
prominent classes of Frobenius algebras, the Hecke algebras of Coxeter
groups, and the finite dimensional Hopf algebras over fields are exhibited.

This volume is self contained and the only prerequisite is a basic knowledge
of linear algebra. 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 as
mathematicians working in other fields.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students starting research in the representation theory of algebras as well as mathematicians working in other fields.