Quantization of Hamiltonian-type Lie algebras

Abstract

In a previous paper, we classified all Lie bialgebras structures of Hamiltonian type. In this paper, we give an explicit formula for the quantization of Hamiltonian-type Lie algebras.

Lie bialgebra structures on the extended affine Lie algebra sl2(CqXu1, Li2 2013Journal of Pure and Applied Algebra4000View full textAdd to dashboardCite

“…Lie bialgebra structures on the Witt algebra and the Virasoro algebra were considered and classified in [21,25]. Since then, Lie bialgebra structures as well as their quantizations on some infinitedimensional graded Lie algebras, in particular those containing the Virasoro algebra (or its q-analog) have been extensively studied (e.g., [7,13,17,19,22,23,[25][26][27][28]). We have noticed that, for the above-mentioned infinite-dimensional graded Lie algebras, the Virasoro algebra plays a very crucial role in determining their bialgebra structures because of the fact that the modules of the intermediate series of the Virasoro algebra have relatively simple module structures (see, e.g., [24]).…”

Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$

“…Lie bialgebra structures on the Witt algebra and the Virasoro algebra were considered and classified in [22,26]. Since then, Lie bialgebra structures as well as their quantizations on some infinite-dimensional graded Lie algebras, in particular those containing the Virasoro algebra (or its q-analog) have been extensively studied (e.g., [7,13,17,19,23,24,[26][27][28][29]). We have noticed that, for the above-mentioned infinite-dimensional graded Lie algebras, the Virasoro algebra plays a very crucial role in determining their bialgebra structures because of the fact that the modules of the intermediate series of the Virasoro algebra have relatively simple module structures (see, e.g., [25]).…”