Quantum seaweed algebras and quantization of affine Cremmer-Gervais r-matrices

Details Quantum seaweed algebras and quantization of affine Cremmer-Gervais r-matrices Quantum seaweed algebras and quantization of affine Cremmer-Gervais r-matrices

2006-05-09

arxiv.org/abs/math/0605236v1

Mathematics

Quantum Algebra

16 pages

Scientific paper

We propose a method of quantization of certain Lie bialgebra structures on the polynomial Lie algebras related to quasi-trigonometric solutions of the classical Yang--Baxter equation. The method is based on an affine realization of certain seaweed algebras and their quantum analogues. We also propose a method of $\omega$-affinization, which enables us to quantize rational $r$-matrices of $\mathfrak{sl}(3)$.

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