scholarly journals Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology

2016 ◽  
Vol 243 (1151) ◽  
pp. 0-0
Author(s):  
Reiner Hermann
Keyword(s):  
Hochschild Cohomology ◽  
Monoidal Categories ◽  
Gerstenhaber Bracket

scholarly journals $A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology

2020 ◽  
Vol 14 (2) ◽  
pp. 531-565
Author(s):  
Cris Negron ◽  
Yury Volkov ◽  
Sarah Witherspoon
Keyword(s):  
Hochschild Cohomology ◽  
Gerstenhaber Bracket

scholarly journals Gerstenhaber Bracket on the Hochschild Cohomology via An Arbitrary Resolution

2019 ◽  
Vol 62 (3) ◽  
pp. 817-836 ◽  
Author(s):  
Yury Volkov
Keyword(s):  
Hochschild Cohomology ◽  
Short Proof ◽  
Hochschild Homology ◽  
Full Description ◽  
Algebra Structure ◽  
Bimodule Resolution ◽  
Symmetric Algebras ◽  
Gerstenhaber Algebra ◽  
Different Types ◽  
Gerstenhaber Bracket

AbstractWe prove formulas of different types that allow us to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology. We also give some new formulas for the Connes differential on the Hochschild homology that lead to formulas for the Batalin–Vilkovisky (BV) differential on the Hochschild cohomology in the case of symmetric algebras. Finally, we use one of the obtained formulas to provide a full description of the BV structure and, correspondingly, the Gerstenhaber algebra structure on the Hochschild cohomology of a class of symmetric algebras.

scholarly journals Hochschild cohomology and “smoothness” in monoidal categories

2007 ◽  
Vol 208 (1) ◽  
pp. 297-330 ◽  
Author(s):  
A. Ardizzoni ◽  
C. Menini ◽  
D. Ştefan
Keyword(s):  
Hochschild Cohomology ◽  
Monoidal Categories

scholarly journals Hochschild Cohomology, Monoid Objects and Monoidal Categories

2020 ◽  
Author(s):  
Magnus Hellstrøm-Finnsen
Keyword(s):  
Hochschild Cohomology ◽  
Abelian Groups ◽  
Cochain Complex ◽  
Monoidal Categories ◽  
Equivalent Formulation ◽  
Theoretical Formulation ◽  
Cohomology Monoid

Abstract This paper expands further on a category theoretical formulation of Hochschild cohomology for monoid objects in monoidal categories enriched over abelian groups, which has been studied in Hellstrøm-Finnsen (Commun Algebra 46(12):5202–5233, 2018). This topic was also presented at ISCRA, Isfahan, Iran, April 2019. The present paper aims to provide a more intuitive formulation of the Hochschild cochain complex and extend the definition to Hochschild cohomology with values in a bimodule object. In addition, an equivalent formulation of the Hochschild cochain complex in terms of a cosimplicial object in the category of abelian groups is provided.

scholarly journals The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras

2021 ◽  
Vol 580 ◽  
pp. 264-298
Author(s):  
Joanna Meinel ◽  
Van C. Nguyen ◽  
Bregje Pauwels ◽  
María Julia Redondo ◽  
Andrea Solotar
Keyword(s):  
Hochschild Cohomology ◽  
Special Biserial Algebras

scholarly journals Going from cohomology to Hochschild cohomology

2005 ◽  
Vol 288 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Emil Sköldberg
Keyword(s):  
Hochschild Cohomology
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