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Homological invariants of generalized bound path algebras

Viktor Chust, Flávio U. Coelho

Abstract

We study some homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. We discuss the particular case where the algebra is a generalized path algebra and give conditions for those algebras to be shod or quasitilted.

Homological invariants of generalized bound path algebras

Abstract

We study some homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. We discuss the particular case where the algebra is a generalized path algebra and give conditions for those algebras to be shod or quasitilted.
Paper Structure (16 sections, 14 theorems, 41 equations)

This paper contains 16 sections, 14 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Path algebras
  4. Generalized bound path algebras (gbp-algebras)
  5. Representations
  6. Realizing an $A_i$-module as a $\Lambda$-module
  7. Homological dimensions
  8. First case
  9. Cones and duals
  10. General case
  11. Homological dimensions for gbp-algebras
  12. A special kind of gbp-algebras
  13. Opposite algebras
  14. Finitistic dimension
  15. Homological dimensions for gp-algebras
  16. ...and 1 more sections

Key Result

Theorem 2.2

There is a $k$-linear equivalence which restricts to an equivalence

Theorems & Definitions (29)

  • Definition 2.1
  • Theorem 2.2: CC2, see also ICNLP
  • Proposition 2.3
  • Lemma 3.1
  • proof
  • Corollary 3.2
  • Lemma 3.3
  • proof
  • Definition 3.4
  • Proposition 3.5
  • ...and 19 more