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Golod-Shafarevich-Vinberg type theorems and finiteness conditions for potential algebras (2201.04479v1)
Published 12 Jan 2022 in math.RA, math-ph, math.AG, math.GR, and math.MP
Abstract: We obtain a lower estimate for the Hilbert series of Jacobi algebras and their completions by providing analogue of the Golog-Shafarevich-Vinberg theorem for potential case. We especially treat non-homogeneous situation. This estimate allows to answer number of questions arising in the work of Wemyss-Donovan-Brown on noncommutative singularities and deformation theory. In particular, we prove that the only case when a potential algebra or its completion could be finite dimensional or of linear growth, is the case of two variables and potential having terms of degree three.