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Frobenius Algebras I
EMS Textbooks in Mathematics

Andrzej Skowroński (Nicolaus Copernicus University, Toruń, Poland)
Kunio Yamagata (Tokyo University of Agriculture and Technology, Japan)

Frobenius Algebras I

Basic Representation Theory

ISBN print 978-3-03719-102-6, ISBN online 978-3-03719-602-1
DOI 10.4171/102
December 2011, 661 pages, hardcover, 16.5 x 23.5 cm.
58.00 Euro

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 mathematicians working in other fields.

Keywords: Algebra, module, representation, quiver, ideal, radical, simple module, semisimple module, uniserial module, projective module, injective module, simple algebra, semisimple algebra, separable algebra, hereditary algebra, Nakayama algebra, Frobenius algebra, symmetric algebra, selfinjective algebra, Brauer tree algebra, enveloping algebra, Coxeter group, Coxeter graph, Hecke algebra, coalgebra, comodule, Hopf algebra, Hopf module, syzygy module, periodic module, periodic algebra, irreducible homomorphism, almost split sequence, Auslander–Reiten translation, Auslander–Reiten quiver, extension spaces, projective dimension, injective dimension, category, functor, Nakayama functor, Nakayama automorphism, Morita equivalence, Morita–Azumaya duality

Further Information

Review in Zentralblatt MATH 05988530

Review in MR 2894798

Review in MAA Reviews