2022/01/12 by Natalia Iyudu, Iyudu, Natalia, Stanislav Shkarin +1
Mathematics · #16A22 #17A45 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2201.04479
openalex publication_date 2022/01/12 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
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.