Mathematics – Rings and Algebras
Scientific paper
2005-06-09
Mathematics
Rings and Algebras
Misprints and a few minor mistakes has been corrected
Scientific paper
In this paper we apply a method devised in \cite{HartLarsSilv1D,LarsSilv1D} to the three-dimensional simple Lie algebra $\sll$. One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present paper that when our deformation scheme is applied to $\sll$ we can, by choosing parameters suitably, deform $\sll$ into the Heisenberg Lie algebra and some other three-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where $\sll$ is rigid. The resulting algebras are quadratic and we point out possible connections to ``geometric quadratic algebras'' such as the Artin--Schelter regular algebras, studied extensively since the beginning of the 90's in connection with non-commutative projective geometry.
Larsson Daniel
Silvestrov Sergei D.
No associations
LandOfFree
Quasi-Deformations of sl_2(\F) using twisted derivations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quasi-Deformations of sl_2(\F) using twisted derivations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi-Deformations of sl_2(\F) using twisted derivations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-170648