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Basic Representation Theory of Algebras (Hardcover, 1st ed. 2020)
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Basic Representation Theory of Algebras (Hardcover, 1st ed. 2020)
Series: Graduate Texts in Mathematics, 283
Expected to ship within 9 - 15 working days
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This textbook introduces the representation theory of algebras by
focusing on two of its most important aspects: the Auslander-Reiten
theory and the study of the radical of a module category. It starts
by introducing and describing several characterisations of the
radical of a module category, then presents the central concepts of
irreducible morphisms and almost split sequences, before providing
the definition of the Auslander-Reiten quiver, which encodes much
of the information on the module category. It then turns to the
study of endomorphism algebras, leading on one hand to the
definition of the Auslander algebra and on the other to tilting
theory. The book ends with selected properties of
representation-finite algebras, which are now the best understood
class of algebras. Intended for graduate students in representation
theory, this book is also of interest to any mathematician wanting
to learn the fundamentals of this rapidly growing field. A graduate
course in non-commutative or homological algebra, which is standard
in most universities, is a prerequisite for readers of this book.
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