Two-dimensional tame and maximal orders of finite representation type / Idun Reiten and Michel Van den Bergh.

Format:

Book

Author/Creator:

Reiten, Idun, 1942- author.

Bergh, M. van den, author.

Series:

Memoirs of the American Mathematical Society ; Volume 80, Number 408.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 80, Number 408

Language:

English

Subjects (All):

Associative algebras.

Representations of algebras.

Grothendieck groups.

Physical Description:

1 online resource (85 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island, United States : American Mathematical Society, 1989.

Language Note:

English

Contents:

""TABLE OF CONTENTS""; ""INTRODUCTION""; ""1. TAME AND MAXIMAL ORDERS AND THEIR GROTHENDIECK GROUPS""; ""1.1 Orders""; ""1.2 Reflexive Morita equivalence""; ""1.3 Grothendieck group of tame and maximal orders""; ""2. THE ASSOCIATED GRADED ORDERS""; ""2.1 The shape of the Auslander-Reiten quivers""; ""2.2 The associated graded algebras""; ""2.3 The isomorphism classes of the path algebras with quadratic relations""; ""2.4 Properties of the path algebras with quadratic relations and their completions""; ""2.5 The classification for gr Î?""; ""2.6 k[[x[sub(1)],x[sub(2)]]]-algebras""

""2.7 General comments on existence of almost split sequences""""3. THE LATTICE OF OVERLYING ORDERS""; ""3.1 The Grothendieck group of a translation quiver""; ""3.2 Admissible sets and zero sets""; ""3.3 Zero sets of tame orders""; ""3.4 When are Î? and End [sub(Î?)] (M) reflexive Morita equivalent?""; ""3.5 AR-quivers for overorders""; ""3.6 Relationship between K[sub(0)](mod[sub(1)] Î?) and K[sub(0)](mod Î?)""; ""4. MAXIMAL ORDERS OF FINITE REPRESENTATION TYPE""; ""4.1 The method""; ""4.2 The universal covering of Î? is ZD[sub(n)]""; ""4.3 The universal covering is ZE[sub(i)]""

Notes:

"July 1989, Volume 80, Number 408 (fourth of 5 numbers)"--Cover.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0831-7