Journal de théorie et applications du mensonge généralisé

Quasi-Lie deformations on the algebra F[t]/(tN) 1

Abstract

Daniel LARSSON , Gunnar SIGURDSSON , and Sergei D. SILVESTROV

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.