Elliptic R-matrices and Feigin and Odesskii’s elliptic algebras

The algebras $$Q_{n,k}(E,\tau )$$ introduced by Feigin and Odesskii as generalizations of the 4-dimensional Sklyanin form a family quadratic parametrized coprime integers $$n>k\ge 1$$ , complex elliptic curve E, point $$\tau \in E$$ . main result in this paper is that has same Hilbert series polynomial ring on n variables when $$ not torsion point. We also show Koszul algebra, hence global dimension point, and, for all but countably many Artin–Schelter regular. proofs use fact space relations defining image an operator $$R_{\tau }(\tau belongs to operators }(z):{\mathbb {C}}^n\otimes {\mathbb {C}}^n\rightarrow {C}}^n$$ $$z\in {C}}$$ (we will show) satisfy quantum Yang–Baxter equation with spectral parameter.