On support varieties and tensor products for finite dimensional algebras

It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can exist. In particular, we show that for certain quantum complete intersections, the...

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Bibliographic Details
Published in:Journal of algebra 2020-04, Vol.547, p.226-237
Main Authors: Bergh, Petter Andreas, Hustad Sandøy, Mads, Solberg, Øyvind
Format: Article
Language:English
Subjects:
Quantum complete intersections
Support varieties
Tensor products
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Summary:It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can exist. In particular, we show that for certain quantum complete intersections, there are modules and bimodules for which the variety of the tensor product is not even contained in the variety of the one-sided module.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2019.10.059