12 citations · 64 across the 40 of their papers we have counts for
41 papers
Golod-Shafarevich-Vinberg type theorems and finiteness conditions for potential algebras
Natalia Iyudu, Stanislav Shkarin
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 esp…
Sklyanin algebras and a cubic root of 1
Natalia Iyudu, Stanislav Shkarin
We consider Sklyanin algebras with 3 generators, which are quadratic algebras over a field $\K$ with generators given by relations , $pyz+qzy+rxx…
Classification of quadratic and cubic PBW algebras on three generators
Natalia Iyudu, Stanislav Shkarin
We give a complete classification of quadratic algebras A, with Hilbert series , which is the Hilbert series of commutative polynomials on 3 variables. Koszul algeb…
Potential algebras with few generators
Natalia Iyudu, Stanislav Shkarin
We give a complete description of quadratic potential and twisted potential algebras on 3 generators as well as cubic potential and twisted potential algebras on 2 generators up to…
Quadratic automaton algebras and intermediate growth
Natalia Iyudu, Stanislav Shkarin
We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its…
Two problems from the Polishchuk and Positselski book on Quadratic algebras
Natalia Iyudu, Stanislav Shkarin
In the book 'Quadratic algebras' by Polishchuk and Positselski [23] algebras with a small number of generators (n=2,3) are considered. For some number r of relations possible Hilbe…