Cremmer‐Gervais quantum Lie algebra

Abstract

We describe a quantum Lie algebra based on the Cremmer-Gervais R-matrix. The algebra arises upon a restriction of an infinite-dimensional quantum Lie algebra.

Drinfeld-Jimbo Quantum Lie Algebra

“…An important class of braidings arises as quantizations [8,11] of classical r-matrices corresponding to Belavin-Drinfeld triples [3]. The problem of a description of quantum Lie algebras compatible with the Cremmer-Gervais R-matrix [6] has been addressed in our previous work [15] with the help of a suitable rime Ansatz [14]. The Cremmer-Gervais R-matrix corresponds to a maximal Belavin-Drinfeld triple for the defining fundamental representation of the quantum group of type GL.…”