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- W3036681138 abstract "The algebras $$Q_{n,k}(E,tau )$$ introduced by Feigin and Odesskii as generalizations of the 4-dimensional Sklyanin algebras form a family of quadratic algebras parametrized by coprime integers $$n>kge 1$$ , a complex elliptic curve E, and a point $$tau in E$$ . The main result in this paper is that $$Q_{n,k}(E,tau )$$ has the same Hilbert series as the polynomial ring on n variables when $$tau $$ is not a torsion point. We also show that $$Q_{n,k}(E,tau )$$ is a Koszul algebra, hence of global dimension n when $$tau $$ is not a torsion point, and, for all but countably many $$tau $$ , $$Q_{n,k}(E,tau )$$ is Artin–Schelter regular. The proofs use the fact that the space of quadratic relations defining $$Q_{n,k}(E,tau )$$ is the image of an operator $$R_{tau }(tau )$$ that belongs to a family of operators $$R_{tau }(z):{mathbb {C}}^notimes {mathbb {C}}^nrightarrow {mathbb {C}}^notimes {mathbb {C}}^n$$ , $$zin {mathbb {C}}$$ , that (we will show) satisfy the quantum Yang–Baxter equation with spectral parameter." @default.
- W3036681138 created "2020-06-25" @default.
- W3036681138 creator A5064788406 @default.
- W3036681138 creator A5076253324 @default.
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- W3036681138 date "2023-03-21" @default.
- W3036681138 modified "2023-09-23" @default.
- W3036681138 title "Elliptic R-matrices and Feigin and Odesskii’s elliptic algebras" @default.
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- W3036681138 doi "https://doi.org/10.1007/s00029-023-00827-0" @default.
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