2005/06/09 by Daniel Larsson, Larsson, Daniel, Sergei Silvestrov +1 · 1 citation
Mathematics · Physics and Astronomy · #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.math/0506172
openalex publication_date 2005/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we apply a method devised in \citeHartLarsSilv1D,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.