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
2019 ◽  
Vol 62 (3) ◽  
pp. 817-836 ◽  
Author(s):  
Yury Volkov

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.


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

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

2017 ◽  
Vol 11 (4) ◽  
pp. 1351-1379 ◽  
Author(s):  
Lauren Grimley ◽  
Van Nguyen ◽  
Sarah Witherspoon

1998 ◽  
Vol 205 (2) ◽  
pp. 391-412 ◽  
Author(s):  
Karin Erdmann ◽  
Nicole Snashall

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