QuasibomLie algebras, central extensions and 2cocyclelike identities
(2005) In Journal of Algebra 288(2). p.321344 Abstract
 This paper introduces the notion of a quasihomLie algebra, or simply, a qhlalgebra, which is a natural generalization of homLie algebras introduced in a previous paper [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using sigmaderivations, math. QA/0408064]. QuasihomLie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skewsymmetry. The natural realm for these quasihomLie algebras is generalizationsdeformations of the Witt algebra delta of derivations on the Laurent polynomials C[t,t(1)]. We also develop a theory of central extensions for qhlalgebras which can be used to deform and generalize... (More)
 This paper introduces the notion of a quasihomLie algebra, or simply, a qhlalgebra, which is a natural generalization of homLie algebras introduced in a previous paper [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using sigmaderivations, math. QA/0408064]. QuasihomLie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skewsymmetry. The natural realm for these quasihomLie algebras is generalizationsdeformations of the Witt algebra delta of derivations on the Laurent polynomials C[t,t(1)]. We also develop a theory of central extensions for qhlalgebras which can be used to deform and generalize the Virasoro algebra by centrally extending the deformed Witt type algebras constructed here. In addition, we give a number of other interesting examples of quasihomLie algebras, among them a deformation of the loop algebra. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/237454
 author
 Larsson, Daniel ^{LU} and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2005
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Loop algebras, Witt algebras, algebras, (color) Lie, quasihomLie algebras, deformations, central extensions, Virasoro algebras
 in
 Journal of Algebra
 volume
 288
 issue
 2
 pages
 321  344
 publisher
 Elsevier
 external identifiers

 wos:000229514700004
 scopus:18744416558
 ISSN
 00218693
 DOI
 10.1016/j.jalgebra.2005.02.032
 language
 English
 LU publication?
 yes
 id
 66facc7f51fb4533b2b502cd89df4f9a (old id 237454)
 date added to LUP
 20070823 08:46:45
 date last changed
 20180304 03:36:03
@article{66facc7f51fb4533b2b502cd89df4f9a, abstract = {This paper introduces the notion of a quasihomLie algebra, or simply, a qhlalgebra, which is a natural generalization of homLie algebras introduced in a previous paper [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using sigmaderivations, math. QA/0408064]. QuasihomLie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skewsymmetry. The natural realm for these quasihomLie algebras is generalizationsdeformations of the Witt algebra delta of derivations on the Laurent polynomials C[t,t(1)]. We also develop a theory of central extensions for qhlalgebras which can be used to deform and generalize the Virasoro algebra by centrally extending the deformed Witt type algebras constructed here. In addition, we give a number of other interesting examples of quasihomLie algebras, among them a deformation of the loop algebra.}, author = {Larsson, Daniel and Silvestrov, Sergei}, issn = {00218693}, keyword = {Loop algebras,Witt algebras,algebras,(color) Lie,quasihomLie algebras,deformations,central extensions,Virasoro algebras}, language = {eng}, number = {2}, pages = {321344}, publisher = {Elsevier}, series = {Journal of Algebra}, title = {QuasibomLie algebras, central extensions and 2cocyclelike identities}, url = {http://dx.doi.org/10.1016/j.jalgebra.2005.02.032}, volume = {288}, year = {2005}, }