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The Hochschild cohomology groups under gluing arrows

Yuming Liu, Lleonard Rubio y Degrassi, Can Wen

Abstract

In a previous paper arXiv:2211.05435 we have compared the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two idempotents. In the present paper, we compare the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two arrows.

The Hochschild cohomology groups under gluing arrows

Abstract

In a previous paper arXiv:2211.05435 we have compared the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two idempotents. In the present paper, we compare the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two arrows.
Paper Structure (7 sections, 26 theorems, 81 equations)

This paper contains 7 sections, 26 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. First Hochschild cohomology
  4. Center
  5. Fundamental group
  6. Higher degrees
  7. Examples

Key Result

Lemma 2.9

Let $B$ be a subalgebra of a finite dimensional algebra $A$ obtained by gluing two arrows $\alpha$ and $\beta$ of $Q_A$. For $\eta,\delta\in (Q_A)_1$, the following statements hold.

Theorems & Definitions (79)

  • Example 2.1
  • Example 2.2
  • Example 2.3
  • Remark 2.4
  • Remark 2.5
  • Definition 2.6
  • Definition 2.7
  • Remark 2.8
  • Lemma 2.9
  • Proposition 2.10
  • ...and 69 more