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

Samsonov, M.; Stolin, A.; Tolstoy, V.

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

Authors

Samsonov, M.

Stolin, A.

Tolstoy, V.

Description

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 $ω$-affinization, which enables us to quantize rational $r$-matrices of $\mathfrak{sl}(3)$.
16 pages