Schrödinger-Virasoro type Lie bialgebra: a twisted case

Abstract

In this paper, we investigate Lie bialgebra structures on a twisted Schrödinger-Virasoro type algebra L. All Lie bialgebra structures on L are triangular coboundary, which is different from the relative result on the original Schrödinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to L ⊗ L and we develop one method to search them.

Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras

“…Then Claim 5 holds for the case s = 1 2 . Similar to the proof of Claim 3 of [3], we can prove this claim also holds for the case s = 0. This claim follows from Lemmas 3.2, 2.6, 2.7 and Claims 4, 5.…”

“…Lie superbialgebra structures on Supported by the NSF grant 11101056 of China the Ramond N = 2 super Virasoro algebra were considered in [33]. The Lie bialgebra structures on the original case L 1 2 0 (with c = 0) and a twisted case L 0 −3 (with c = 0) were respectively investigated by [6] and [3]. In this paper we shall investigate Lie bialgebra structures on L s λ mainly using the techniques introduced recently in [13].…”

“…The Lie bialgebra structures on the Schrödinger-Virasoro Lie algebras L 0 −3 and L 1 2 0 have already been considered respectively in [3] and [6] (with c = 0). We just need to consider the following cases:…”

“…0 have already been considered respectively in [3] and [6] (with c = 0). We just need to consider the following cases:…”

Non-weight modules over a Schr{ö}dinger-Virasoro type algebra

“…There also have been some works only on tsv. Lie bialgebra structures, modules of the intermediate series, the Lie conformal algebra and quantization of tsv were studied in [7,6,22,24] respectively. From these results, it is found that tsv has some particular properties which are different from many other cases of the twisted deformative Schrödinger-Virasoro Lie algebras.…”