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Hochschild cohomology of some quantum complete intersections

Abstract:
We compute the Hochschild cohomology ring of the algebras $A= k\langle X, Y\rangle/ (X^a, XY-qYX, Y^a)$ over a field $k$ where $a\geq 2$ and where $q\in k$ is a primitive $a$-th root of unity. We find the the dimension of $\mathrm{HH}^n(A)$ and show that it is independent of $a$. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/S0219498818502158

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Somerville College
Role:
Author
Publisher:
World Scientific Publishing
Journal:
Journal of Algebra and its Applications More from this journal
Volume:
17
Issue:
11
Article number:
1850215
Publication date:
2018-01-04
Acceptance date:
2017-11-02
DOI:
EISSN:
1793-6829
ISSN:
0219-4988
Keywords:
Pubs id:
pubs:742602
UUID:
uuid:d50ede46-2004-4d8b-a6aa-496ce85c29bc
Local pid:
pubs:742602
Source identifiers:
742602
Deposit date:
2017-11-03

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