Journal of Nonlinear Mathematical Physics

Volume 23, Issue 1, January 2016, Pages 47 - 73

Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

Authors
Mahouton Norbert Hounkonnou1, *, Partha Guha2, Tudor Ratiu3
1University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), 072 B.P. 50 Cotonou, Republic of Benin,norbert.hounkonnou@cipma.uac.bj
2S. N. Bose National Centre for Basic Sciences, JD Block, Sector - 3, 700098, Salt Lake, Calcutta, India,parthaguh@gmail.com
3Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne. Switzerland,tudor.ratiu@epfl.ch
*Corresponding author: with copy to hounkonnou@yahoo.fr
Corresponding Author
Mahouton Norbert Hounkonnou
Received 15 June 2015, Accepted 16 October 2015, Available Online 6 January 2021.
DOI
10.1080/14029251.2016.1135642How to use a DOI?
Keywords
Virasoro algebra; Left-symmetric algebras; Quasi-associativity; Coboundary operators; Nonlinear systems of hydrodynamic type
Abstract

Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 –245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quasi-associative. Its link to geometry and nonlinear systems of hydrodynamic type is also recalled. Further, the criteria of skew-symmetry, derivation and Jacobi identity making this algebra into a Lie algebra are derived. The coboundary operators are defined and discussed. We deduce the hereditary operator and its generalization to the corresponding 3–ary bracket. Further, we derive the so-called ρ–compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated.

Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 1
Pages
47 - 73
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2016.1135642How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Mahouton Norbert Hounkonnou
AU  - Partha Guha
AU  - Tudor Ratiu
PY  - 2021
DA  - 2021/01/06
TI  - Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties
JO  - Journal of Nonlinear Mathematical Physics
SP  - 47
EP  - 73
VL  - 23
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1135642
DO  - 10.1080/14029251.2016.1135642
ID  - Hounkonnou2021
ER  -