5,676 research outputs found
Cremmer-Gervais r-matrices and the Cherednik Algebras of type GL2
We give an intepretation of the Cremmer-Gervais r-matrices for sl(n) in terms
of actions of elements in the rational and trigonometric Cherednik algebras of
type GL2 on certain subspaces of their polynomial representations. This is used
to compute the nilpotency index of the Jordanian r-matrices, thus answering a
question of Gerstenhaber and Giaquinto. We also give an interpretation of the
Cremmer-Gervais quantization in terms of the corresponding double affine Hecke
algebra.Comment: 6 page
Meander graphs and Frobenius Seaweed Lie algebras
The index of a seaweed Lie algebra can be computed from its associated
meander graph. We examine this graph in several ways with a goal of determining
families of Frobenius (index zero) seaweed algebras. Our analysis gives two new
families of Frobenius seaweed algebras as well as elementary proofs of known
families of such Lie algebras.Comment: 5 figures, to appear in Journal of Generalized Lie Theor
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