Support varieties for finite tensor categories: Complexity, realization, and connectedness

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension. Then we show that every conical subvariety of the support v...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2021-09, Vol.225 (9), p.106705, Article 106705
Main Authors: Bergh, Petter Andreas, Plavnik, Julia Yael, Witherspoon, Sarah
Format: Article
Language:English
Subjects:
Finite tensor category
Indecomposable object
Nonsemisimple Hopf algebra
Projective objects
Support varieties
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Summary:We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension. Then we show that every conical subvariety of the support variety of the unit object may be realized as the support variety of an object. Finally, we show that the support variety of an indecomposable object is connected.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2021.106705