december 2023 A module structure on Hochschild cohomology of coideal subalgebras
Liyu Liu, Lingchao Meng
Bull. Belg. Math. Soc. Simon Stevin 30(4): 445-455 (december 2023). DOI: 10.36045/j.bbms.220829

Abstract

Let $B$ be a right coideal subalgebra of a Hopf algebra $H$. We construct a left $H^*$-module structure on the Hochschild cohomology of $B$ with coefficients in $B\otimes M$ where $M$ is a $B$-bimodule as well as a right $H$-comodule satisfying a compatible condition. We prove that the structure is a canonical invariant which coincides with one given by Krähmer (2012) for quantum homogeneous spaces. In particular, Krähmer's group-like element turns out to be determined by $B$ uniquely, which plays an important role in describing the dualizing complex of $B$.

Citation

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Liyu Liu. Lingchao Meng. "A module structure on Hochschild cohomology of coideal subalgebras." Bull. Belg. Math. Soc. Simon Stevin 30 (4) 445 - 455, december 2023. https://doi.org/10.36045/j.bbms.220829

Information

Published: december 2023
First available in Project Euclid: 31 December 2023

Digital Object Identifier: 10.36045/j.bbms.220829

Subjects:
Primary: 16E40 , 16T05 , 16T15

Keywords: homological invariant , Hopf algebra , quantum homogeneous space

Rights: Copyright © 2023 The Belgian Mathematical Society

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Vol.30 • No. 4 • december 2023
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