On some almost quadratic algebras coming from twisted derivations
2006 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, Vol. 13, 76-86 p.Article in journal (Refereed) Published
This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(F) for specific choices of the involved parameters and underlying algebras. One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl(2)(F) is rigid.
Place, publisher, year, edition, pages
2006. Vol. 13, 76-86 p.
quasi-hom-Lie algebras, hom-Lie algebras, colour Lie algebras, quasi-deformation, sigma-derivations, extensions, twisted Jacobi identities, almost quadratic algebras.
IdentifiersURN: urn:nbn:se:kth:diva-41444DOI: 10.2991/jnmp.2006.13.Supplement.9ISI: 000241392500010ScopusID: 2-s2.0-33747686517OAI: oai:DiVA.org:kth-41444DiVA: diva2:443875
Baltic-Nordic Workshop on Algebra, Geometry and Mathematical Physics. Tallinn, Estonia. OCT , 2005
QC 201109272011-09-272011-09-272012-10-10Bibliographically approved