Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Representation-finite tensor product of simply connected algebras

Kengo Miyamoto, Qi Wang

Abstract

We determine the representation-finiteness of $A\otimes B$, where both $A$ and $B$ are simply connected algebras with at least three simple modules.

Representation-finite tensor product of simply connected algebras

Abstract

We determine the representation-finiteness of , where both and are simply connected algebras with at least three simple modules.

Paper Structure

This paper contains 15 sections, 36 theorems, 33 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Tensor product of algebras
  4. Simply connected algebra
  5. Tame concealed algebra
  6. Tits form
  7. Reduction theorems
  8. Hereditary algebras
  9. Path algebra of type $A$
  10. Path algebra of type $D$
  11. Result
  12. Nakayama algebras
  13. $B$ is Nakayama
  14. $B$ is not Nakayama
  15. Minimal representation-infinite cases

Key Result

Proposition \oldthetheorem

Let $A$, $B$ and $C$ be bound quiver algebras. Then,

Theorems & Definitions (65)

  • Proposition \oldthetheorem: L-rep-type
  • Proposition \oldthetheorem
  • proof
  • Definition \oldthetheorem: AS
  • Proposition \oldthetheorem: L-rep-type
  • Proposition \oldthetheorem: ASS
  • Definition \oldthetheorem
  • Definition \oldthetheorem
  • Proposition \oldthetheorem: HV
  • Remark \oldthetheorem
  • ...and 55 more