This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
This volume presents the proceedings of a conference hosted by the American School of Classical Studies, Athens and the Deutsches Archäologisches Institut, Athens in 2004. There are additional contributions from Patricia Butz, Robin Osborne, Katherine Schwab, Justin St. P. Walsh, Hilda Westervelt and Lorenz Winkler-Horacek. The contents are divided into four sections I. Structure and Ornament; II. Technique and Agency; III. Myth and Narrative and IV. Diffusion and Influence. Highlights include Robin Osbornes discussion of What you can do with a chariot but cant do with a satyr on a Greek temple; Ralf von den Hoffs consideration of the Athenian treasury at Delphi; and Katherine Schwabs presentation of New evidence for Parthenon east metope 14. The papers not only cover a great variety of issues in architectural sculpture but also present a range of case studies from all over the Greek world. The result is an important collection of current research.
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