Hochschild cohomology of Fermat type polynomials with non-abelian\n symmetries

2020/11/11 by Alexey Basalaev, Basalaev, Alexey, A. N. Ionov +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2011.05937

openalex publication_date 2020/11/11 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

For a polynomial f = x₁ⁿ + \… + x_Nⁿ let G_f be the non--abelian\nmaximal group of symmetries of f. This is a group generated by all g \∈\n\GL(N,\ℂ), rescaling and permuting the variables, so that\nf(\x) = f(g \⋅ \x). For any G \⊆ G_f we compute\nexplicitly Hochschild cohomology of the category of G--equivarint matrix\nfactorizations of f. We introduce the pairing on it showing that it is a\nFrobenius algebra.\n

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