Frobenius Algebras: No. II: Tilted and Hochschild Extension Algebras

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 first 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 fields. 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