Two-Dimensional Tame and Maximal Orders of Finite Representation Type.

Intro -- 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 Λ -- 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 Λ and End [sub(Λ)] (M) reflexive Morita equivalent? -- 3.5 AR-quivers for overorders -- 3.6 Relationship between K[sub(0)](mod[sub(1)] Λ) and K[sub(0)](mod Λ) -- 4. MAXIMAL ORDERS OF FINITE REPRESENTATION TYPE -- 4.1 The method -- 4.2 The universal covering of Γ is ZD[sub(n)] -- 4.3 The universal covering is ZE[sub(i)] -- 4.4 The universal covering is ZA[sup(∞)][sub(∞)] -- 4.5 Noncommutative maximal orders -- 5. PASSING FROM THE GRADED TO THE COMPLETE CASE -- 5.1 Graded methods -- 5.2 Reflexive Galois extensions -- 5.3 Interpretation as skew group ring -- REFERENCES.

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