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math.RA2016★ 2 cited
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…
math.RA2016
Asymptotically optimal -step nilpotency of quadratic algebras and the Fibonacci numbers
Natalia Iyudu, Stanislav Shkarin
It follows from the Golod--Shafarevich theorem that if R is an associative algebra given by n generators and quadratic relations, then R is…
math.RA2016★ 1 cited
Three dimensional Sklyanin algebras and Groebner bases
Natalia Iyudu, Stanislav Shkarin
We consider a Sklyanin algebra S with 3 generators, which is the quadratic algebra over a field k with three generators x,y,z given by three relations pxy+qyx+rzz=0, pyz+qzy+rxx=0…