TAILIEUCHUNG - Hom-Lie 2-superalgebras

Hom-Lie 2-superalgebras can be considered as the categorification of Hom-Lie superalgebras. We give the definition of Hom-Lie 2-superalgebras and study their superderivations. We obtain the representation, deformation, and abelian extensions related to the 2-cocycle and Hom-Nijenhuis operators. | Turk J Math (2016) 40: 1 – 20 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Hom-Lie 2-superalgebras Chunyue WANG1 , Qingcheng ZHANG2,∗, Jizhu NAN3 School of Applied Sciences, Jilin Engineering Normal University, Changchun, . China 2 School of Mathematics and Statistics, Northeast Normal University, Changchun, . China 3 School of Mathematical Sciences, Dalian University of Technology, Dalian, . China 1 Received: • Accepted/Published Online: • Final Version: Abstract: Hom-Lie 2-superalgebras can be considered as the categorification of Hom-Lie superalgebras. We give the definition of Hom-Lie 2-superalgebras and study their superderivations. We obtain the representation, deformation, and abelian extensions related to the 2-cocycle and Hom-Nijenhuis operators. Moreover, we also construct a skeletal (strict) Hom-Lie 2-superalgebra from a Hom-associative Rota–Baxter superalgebra. Key words: Hom-Lie 2-superalgebras, superderivations, representations, deformations, abelian extensions, Homassociative Rota–Baxter superalgebras 1. Introduction Higher categorical structures play an important role in both string theory [2] and physics [9,15]. Some higher categorical structures are obtained by categorifying existing mathematical concepts. One of the simplest higher structures is a categorical vector space, that is, a 2-vector space. A categorical Lie algebra introduced by Baez and Crans [3], which is called a Lie 2-algebra, is a 2-vector space equipped with a skew-symmetric bilinear functor, whose Jacobi identity is replaced by the Jacobiator satisfying some coherence laws of its own. Baez and Crans [3] showed that the category of Lie 2-algebras is equivalent to the category of 2-term L∞ -algebras, so a Lie 2-algebra is often defined by a 2-term L∞ -algebra. Recently, Lie 2-algebra theories have been widely developed [4,5,10,12,14,16–19]. In .

• Toán học
• Hom Lie 2 superalgebras
• Abelian extensions
• Homassociative Rota–Baxter superalgebras
• 2 cocycle
• Hom Nijenhuis operators