Deformations, Contractions and Classification of Lie Algebras of Order 3 TeX Export

@misc{citeulike:530773, abstract = {Lie algebras of order \$F\$ (or \$F-\$Lie algebras) are possible generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). These structures have been used to implement new non-trivial extensions of the Poincar\'e algebra. In this paper we set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3. We then initiated a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on \$\mathfrak{sl}(2,\mathbb C)\$ and \$\mathfrak{iso}(1,3)\$ the four-dimensional Poincar\'e algebra.}, archivePrefix = {arXiv}, author = {Goze, M. and de Traubenberg, Rausch M. and Tanasa, A.}, citeulike-article-id = {530773}, citeulike-linkout-0 = {http://arxiv.org/abs/math-ph/0603008}, citeulike-linkout-1 = {http://arxiv.org/pdf/math-ph/0603008}, eprint = {math-ph/0603008}, keywords = {deformation, fractional\_supersymmetry, lie\_theory}, month = {Mar}, posted-at = {2006-03-04 02:28:35}, priority = {2}, title = {Deformations, Contractions and Classification of Lie Algebras of Order 3}, url = {http://arxiv.org/abs/math-ph/0603008}, year = {2006} }

TY - ELEC ID - citeulike:530773 L3 - citeulike-article-id:530773 N2 - Lie algebras of order $F$ (or $F-$Lie algebras) are possible generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). These structures have been used to implement new non-trivial extensions of the Poincar\'e algebra. In this paper we set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3. We then initiated a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on $\mathfrak{sl}(2,\mathbb C)$ and $\mathfrak{iso}(1,3)$ the four-dimensional Poincar\'e algebra. TI - Deformations, Contractions and Classification of Lie Algebras of Order 3 KW - deformation KW - fractional_supersymmetry KW - lie_theory AU - Goze, M AU - de Traubenberg, Rausch AU - Tanasa, A PY - 2006/Mar/02/ UR - http://arxiv.org/abs/math-ph/0603008 ER -