Quasi-Lie deformations on the algebra F[t]/(tN) 1Daniel LARSSON1, Gunnar SIGURDSSON2, Sergei D. SILVESTROV3,
1Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden, E-mail: [email protected]
2Department of Theoretical Physics, School of Engineering Sciences, Royal Institute of Technology (KTH) – AlbaNova University Center, SE-106 91 Stockholm, Sweden, E-mail: [email protected]
3Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden, E-mail: [email protected]
Received date: December 20, 2007; Accepted date: April 02, 2008
This paper explores the quasi-deformation scheme devised by Hartwig, Larsson and Silvestrov as applied to the simple Lie algebra sl2(F). 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 sl2(F) via representations by twisted derivations on the algebra F[t]/(tN) one obtains interesting new multi-parameter families of almost quadratic algebras.