n-李代数的张量积

Tensor Product of n-Lie Algebras

对一个己知的n-李代数L和一个已知的交换的结合代数A构造了一个n-李代数AL,称为A与L的张量n-李代数,并证明了A与L的导子代数的张量积和A与A的导子代数的张量积都是张量n-李代数的导子代数的子代数.

For a giving n-Lie algebra L and a commutative associative algebra A we construct an n-Lie algebra AL, which is called the tensor n-Lie algebra of A and L. We prove that the tensor product of A and DerL is a subalgebra of the Der（AL）, and the tensor of A and the derivation algebra of A also is a subalgebra of the Der（AL）.