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2014 Constructive Approach to Three Dimensional Sklyanin Algebras
Natalia Iyudu
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J. Gen. Lie Theory Appl. 8(1): 1-2 (2014). DOI: 10.4172/1736-4337.1000e101
Abstract

A three dimensional Sklyanin is the quadratic algebra over a field $\mathbb{k}$ with 3 generators x; y; z given by 3 relations xy - ayx - szz = 0, yz - azy - sxx = 0 and zx - axz - syy = 0, where a,s $\in \mathbb{k}$. A generalized Sklyanin algebra is the algebra given by relations $\mathrm{xy - a_{1}yx - s_{1}zz = 0, yz - a_{2}zy - s_{2}xx = 0 and zx - a_{3}xz - s_{3}yy = 0}$, where $\mathrm{a_{i}, s_{i}} \in \mathbb{k}$. In this paper we announce the following results; the complete proofs will appear elsewhere. We determine explicitly the parameters for which these algebras has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates as well as when these algebras are Koszul and PBW, using constructive combinatorial methods. These provide new direct proofs of results established first by Artin, Tate, and Van Den Bergh.

Iyudu: Constructive Approach to Three Dimensional Sklyanin Algebras
Copyright © 2014 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)
Natalia Iyudu "Constructive Approach to Three Dimensional Sklyanin Algebras," Journal of Generalized Lie Theory and Applications 8(1), 1-2, (2014). https://doi.org/10.4172/1736-4337.1000e101
Published: 2014
Vol.8 • No. 1 • 2014
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