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Gerstenhaber brackets on Hochschild cohomology of general twisted tensor products

Tekin Karadag, Dustin McPhate, Pablo S. Ocal, Tolulope Oke, Sarah Witherspoon

Abstract

We present techniques for computing Gerstenhaber brackets on Hochschild cohomology of general twisted tensor product algebras. These techniques involve twisted tensor product resolutions and are based on recent results on Gerstenhaber brackets expressed on arbitrary bimodule resolutions.

Gerstenhaber brackets on Hochschild cohomology of general twisted tensor products

Abstract

We present techniques for computing Gerstenhaber brackets on Hochschild cohomology of general twisted tensor product algebras. These techniques involve twisted tensor product resolutions and are based on recent results on Gerstenhaber brackets expressed on arbitrary bimodule resolutions.

Paper Structure

This paper contains 4 sections, 8 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. Twisted tensor product algebras and resolutions
  3. Gerstenhaber bracket for twisted tensor products
  4. Jordan plane

Key Result

Theorem 2.3

Let $M,N$ be $A$- and $B$-bimodules that are compatible with a twisting map $\tau: B\otimes A\rightarrow A\otimes B$. Let $P_{\begin{picture}(2.5,2) (1,1)\put(2,2.5){\circle*{2}}\end{picture}}(M)$, $P_{\begin{picture}(2.5,2) (1,1)\put(2,2.5){\circle*{2}}\end{picture}}(N

Theorems & Definitions (13)

  • Definition 2.2
  • Theorem 2.3
  • Theorem 2.5
  • Theorem 2.6
  • proof
  • Theorem 3.3
  • Lemma 3.8
  • proof
  • Lemma 3.9
  • proof
  • ...and 3 more