Hochschild cohomology of Fermat type polynomials with non-abelian symmetries

Alexey Basalaev; Andrei Ionov

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arXiv · 2011.05937

Hochschild cohomology of Fermat type polynomials with non-abelian symmetries

Alexey Basalaev·Andrei Ionov

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Abstract

For a polynomial $f = x_1^n + \dots + x_N^n$ let $G_f$ be the non--abelian maximal group of symmetries of $f$. This is a group generated by all $g \in \mathrm{GL}(N,\mathbb{C})$, rescaling and permuting the variables, so that $f(\mathbf{x}) = f(g \cdot \mathbf{x})$. For any $G \subseteq G_f$ we compute explicitly Hochschild cohomology of the category of $G$--equivarint matrix factorizations of $f$. We introduce the pairing on it showing that it is a Frobenius algebra.

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BibTeX RIS

Alexey Basalaev, Andrei Ionov. 2020-11-11. Hochschild cohomology of Fermat type polynomials with non-abelian symmetries. https://arxiv.org/abs/2011.05937

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