Quasi-Deformations of sl_2(\F) using twisted derivations

• DOI: 10.48550/arxiv.math/0506172
• Publication Date: 2005-01-01
• Authors: Daniel Larsson; Sergei Silvestrov
• Keywords: Quadratic algebra

In this paper we apply a method devised in \cite{HartLarsSilv1D,LarsSilv1D} to the three-dimensional simple Lie algebra $\sll$. One of main points deformation is that deformed comes endowed with canonical twisted Jacobi identity. We show present when our scheme applied $\sll$ can, by choosing parameters suitably, deform into Heisenberg and some other algebras addition more exotic types algebras, being stark contrast classical schemes where rigid. The resulting are quadratic point out possible connections ``geometric algebras'' such as Artin--Schelter regular studied extensively since beginning 90's connection non-commutative projective geometry.