【摘 要】
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q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed.A q-3-Lie algebra (A,[,,]q,[,,]’q,Jq),where q ∈ F and q ≠ 0,is a vecto
【机 构】
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College of Mathematics and Information Science, Hebei University Baoding, Hebei 071002, China
论文部分内容阅读
q-Deformations of 3-Lie algebras and representations of q-3-Lie algebras are discussed.A q-3-Lie algebra (A,[,,]q,[,,]’q,Jq),where q ∈ F and q ≠ 0,is a vector space A over a field F with 3-ary linear multiplications [,,]q and [,,]’q from A(x)3 to A,and a map Jq:A(x)5 → F satisfying the q-Jacobi identity Jq(x1,x2,x3,x4,xs)[x1,x2,[x3,x4,x5]q]’q Jq(x4,x5,x1,x2,x3)[x4,xs,[x1,x2,x3]q]’q for all xi ∈ A.If the multiplications satisfy that [,,]q =[,,]’q and [,,]q is skew-symmetry,then (A,[,,]q,Jq) 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 one-dimensional central extension of q-3-Lie algebras is investigated,and new q-3-Lie algebras (Derq C[x,x-1],[,,]q,[,,]’q,Jq),and (Derδq C[x,x-1],[,,]q,[,,]’q,Jq) are obtained.
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