Witt and Virasoro algebras as lie bialgebras

Lie bialgebra structures on the Schrödinger–Virasoro Lie algebra

“…Since then, many papers on Lie bialgebras appeared, e.g., [3, 11, 13-16, 18, 19, 22, 23]. Witt type Lie bialgebras introduced in [19] were classified in [16], whose generalized cases were considered in [18,22]. Lie bialgebra structures on generalized Virasoro-like and Block Lie algebras were investigated in [23,11].…”

Lie bialgebras of a family of Lie algebras of Block type

“…[3][4][5][6][7][8][9][10]). Lie bialgebras of Witt and Virasoro type were presented in [9]. These types of Lie bialgebras were further classified in [6].…”

Quantization of the q-analog Virasoro-like algebras

“…According to quantum groups theory, a quantum group is essentially a formal deformation of the universal enveloping algebra of a Lie algebra g, the semiclassical structure associated with such a deformation is a Lie bialgebra structure on g. Constructing quantizations of Lie bialgebras is an important method to produce new quantum groups. Using the method twisting the coproduct by a Drinfel'd twist element but keeping the product unchanged, Grunspan [3] presented the quantization of a class of infinite dimensional Lie algebras containing Virasoro algebras studied in [4] (see also [5,6]). Using the same technique, Hu and Wang [7] quantized some Lie algebras presented in [8].…”