Finite-dimensional non-commutative Poisson algebras
Finite-dimensional non-commutative Poisson algebras
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DOI：
10.1016/0022-4049(95)00151-4
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发表时间：
1996-12
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Poisson代数是具有结合代数结构和李代数结构以及莱布尼兹定律的代数。对于有限维的，我们表明，如果他们是半单的结合代数，那么他们是标准的，另一方面，如果他们是半单的李代数，那么他们的结合产品是平凡的。给出了李结构为约化的有限维非交换Poisson代数的结构描述。
Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. For finite-dimensional ones we show that if they are semisimple as associative algebras then they are standard, on the other hand, if they are semisimple as Lie algebras then their associative products are trivial. We also give the descriptions of the structures of finite-dimensional non-commutative Poisson algebras whose Lie structures are reductive.