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- Title
q-Deformations of 3-Lie Algebras.
- Authors
Bai, Ruipu; Lin, Lixin; Zhang, Yan; Kang, Chuangchuang
- Abstract
q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed. A q-3-Lie algebra , where and , is a vector space A over a field 픽 with 3-ary linear multiplications [ , , ] q and from to A, and a map satisfying the q-Jacobi identity for all . If the multiplications satisfy that and is skew-symmetry, then is called a type (I)- q-3- Lie algebra. From q-Lie algebras, group algebras and commutative associative algebras, q-3-Lie algebras and type (I)- q-3-Lie algebras are constructed. Also, the non-trivial onedimensional central extension of q-3-Lie algebras is investigated, and new q-3-Lie algebras , and are obtained.
- Subjects
LIE algebras; JACOBI identity; REPRESENTATIONS of groups (Algebra); LINEAR algebra; TOPOLOGICAL algebras
- Publication
Algebra Colloquium, 2017, Vol 24, Issue 3, p519
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386717000347