Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra
type: Item
instance of: scholarly article
title: Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra
zbMATH Open document ID: 1486.16048
author: Yanyan Li
published in: Electronic Research Archive
publication date: 2021-08-19T00:00:00Z
review text: The Schrödinger-Virasoro Lie algebra \(\mathcal{SV}(\varepsilon)\) is said to be twisted if \(\varepsilon=0\), and to be original if \(\varepsilon=\frac{1}{2}\). The authors complete classify the graded post-Lie algebra structures on \(\mathcal{SV}(0)\), while the corresponding results for \(\mathcal{SV}(\frac{1}{2})\) can be obtained similarly and so are omitted. As an application, the authors characterize the forms of homogeneous Rota-Baxter operators of weight \(1\) on \(\mathcal{SV}(0)\).
reviewed by: Houyi Yu
Mathematics Subject Classification ID: 16W99
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 7383363
zbMATH Keywords: Lie algebra
zbMATH Keywords: post-Lie algebra
zbMATH Keywords: Rota-Baxter operator
zbMATH Keywords: Schrödinger-Virasoro algebra
MaRDI profile type: Publication
Wikidata QID: Q115219064
full work available at URL: era.2021013
OpenAlex ID: W3132468581
cites work: Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
cites work: An analytic problem whose solution follows from a simple algebraic identity
cites work: Left-symmetric algebras, or pre-Lie algebras in geometry and physics
cites work: Affine actions on Lie groups and post-Lie algebra structures
cites work: Commutative post-Lie algebra structures on Lie algebras
cites work: Rota-Baxter operators on Witt and Virasoro algebras
cites work: First Integrals Generated by Pseudosymmetries in Nambu-Poisson Mechanics
cites work: Lie bialgebra structures on the Schrödinger–Virasoro Lie algebra
cites work: Schrödinger invariance and strongly anisotropic critical systems
cites work: Biderivations and commutative post-Lie algebra structure on Schrödinger-Virasoro Lie algebras
cites work: On post-Lie algebras, Lie-Butcher series and moving frames
cites work: PostLie algebra structures on the Lie algebra sl(2,C)
cites work: Novikov algebras and Schrödinger–Virasoro Lie algebras
cites work: The Schrödinger-Virasoro Lie group and algebra: representation theory and cohomological study
cites work: Baxter algebras and combinatorial identities. I
cites work: Q4840174
cites work: Post-Lie algebra structures on the Witt algebra
cites work: Rota-Baxter operators on 4-dimensional complex simple associative algebras
cites work: Q4614822
cites work: On vertex algebra representations of the Schrödinger-Virasoro Lie algebra
cites work: Homology of generalized partition posets
cites work: Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras
DOI: 10.3934/ERA.2021013
description: scientific article; zbMATH DE number 7383363