# Hochschild cohomology of some quantum complete intersections

## Author:

Erdmann, K
Hellstrom-Finnsen, M

November 2018

## Journal:

JOURNAL OF ALGEBRA AND ITS APPLICATIONS

## Last Updated:

2019-08-17T14:51:03.13+01:00

11

17

## DOI:

10.1142/S0219498818502158

1850215-1850215

## abstract:

© 2018 World Scientific Publishing Company. We compute the Hochschild cohomology ring of the algebras A = k(X,Y)/(Xa,XY - qY X,Ya) over a field k where a ≥ 2 and where q k is a primitive ath root of unity. We find the dimension of HHn(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.

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