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Skew category algebras, twisted tensor product algebras and induction of precosheaves

Tiberiu Coconet, Virgilius-Aurelian Minuta, Constantin-Cosmin Todea

Abstract

We show that a skew category algebra can be embedded into a twisted tensor product algebra. We investigate the extension of some concepts of Puig and Turull from group algebras to category algebras and their behavior with respect to skew category algebras.

Skew category algebras, twisted tensor product algebras and induction of precosheaves

Abstract

We show that a skew category algebra can be embedded into a twisted tensor product algebra. We investigate the extension of some concepts of Puig and Turull from group algebras to category algebras and their behavior with respect to skew category algebras.
Paper Structure (8 sections, 12 theorems, 80 equations)

This paper contains 8 sections, 12 theorems, 80 equations.

Table of Contents

  1. Introduction
  2. Skew category algebras, twisted tensor product algebras and proof of Theorem \ref{['thm:11']}
  3. Skew category algebras.
  4. A twisted tensor product on category algebras.
  5. Surjective Turull's induction of precosheaves of k-algebras
  6. Precosheaves of k-algebras and modules over category algebras.
  7. Surjective Turull's induction of precosheaves of k-algebras.
  8. Surjective Puig's induction of interior category algebras and proof of Theorem \ref{['thm:13']}

Key Result

Theorem 1.1

There is an injective homomorphism of $k$-algebras from the skew category algebra into the above twisted tensor product algebra.

Theorems & Definitions (25)

  • Theorem 1.1
  • Corollary 1.2
  • Theorem 1.3
  • Proposition 2.1
  • proof
  • Corollary 2.2
  • proof : Proof of Theorem \ref{['thm:11']}
  • Lemma 3.1
  • Lemma 3.2
  • Definition 3.3
  • ...and 15 more