Non-commutative Poisson algebra structures on affine Kac-Moody algebras
Non-commutative Poisson algebra structures on affine Kac-Moody algebras
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DOI：
10.1016/s0022-4049(96)00141-7
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发表时间：
1998-04
影响因子：
0.8
通讯作者：
F. Kubo
中科院分区：
文献类型：
--
作者：
F. Kubo
非交换泊松代数是具有结合代数结构和李结构以及莱布尼茨定律的代数。研究了无限维代数上的非交换泊松代数结构。我们证明了这些结构在可数维向量空间的所有自同态的结合代数的偏序子代数上是标准的。确定了仿射型Kac-Moody代数上的这些结构。证明了所导出的李理想上的关联积是平凡的，并充分描述了尺度元的关联积作用。
Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie structure together with the Leibniz law. The non-commutative Poisson algebra structures on the infinite-dimensional algebras are studied. We show that these structures are standard on the poset subalgebras of the associative algebra of all endomorphisms of the countable-dimensional vector space. These structures on Kac-Moody algebras of affine type are determined. It is shown that the associative products on the derived Lie ideals are trivial, and the associative product action of the scaling elements are fully described.