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dc.creatorOgievetsky, O.
dc.creatorPopov, T.
dc.date2007-04-16
dc.date2009-05-06
dc.date.accessioned2012-06-08T14:21:29Z
dc.date.available2012-06-08T14:21:29Z
dc.date.issued2012-06-08
dc.identifierhttp://arxiv.org/abs/0704.1947
dc.identifier.urihttps://repositorio.leon.uia.mx/xmlui/123456789/41865
dc.descriptionWe replace the ice Ansatz on matrix solutions of the Yang-Baxter equation by a weaker condition which we call "rime". Rime solutions include the standard Drinfeld-Jimbo R-matrix. Solutions of the Yang--Baxter equation within the rime Ansatz which are maximally different from the standard one we call "strict rime". A strict rime non-unitary solution is parameterized by a projective vector. We show that this solution transforms to the Cremmer-Gervais R-matrix by a change of basis with a matrix containing symmetric functions in the components of the parameterizing vector. A strict unitary solution (the rime Ansatz is well adapted for taking a unitary limit) is shown to be equivalent to a quantization of a classical "boundary" r-matrix of Gerstenhaber and Giaquinto. We analyze the structure of the elementary rime blocks and find, as a by-product, that all non-standard R-matrices of GL(1|1)-type can be uniformly described in a rime form. We discuss then connections of the classical rime solutions with the Bezout operators. The Bezout operators satisfy the (non-)homogeneous associative classical Yang--Baxter equation which is related to the Rota-Baxter operators. We classify the rime Poisson brackets: they form a 3-dimensional pencil. A normal form of each individual member of the pencil depends on the discriminant of a certain quadratic polynomial. We also classify orderable quadratic rime associative algebras. For the standard Drinfeld-Jimbo solution, there is a choice of the multiparameters, for which it can be non-trivially rimed. However, not every Belavin-Drinfeld triple admits a choice of the multiparameters for which it can be rimed. We give a minimal example.
dc.descriptionComment: 50 pages, typos corrected
dc.subjectMathematics - Quantum Algebra
dc.titleR-matrices in Rime
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