与哈密顿算子相关的Lie代数和Balinsky-Novikov代数的例子

Q3 Mathematics

Topological Algebra and its Applications Pub Date : 2018-03-28 DOI:10.1515/taa-2018-0005

O. Artemovych, A. Prykarpatski, D. Blackmore

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引用次数: 4

摘要

摘要我们研究了非结合非交换代数上Poisson括号的代数性质，与它们的乘法结构相容。特别注意李-泊松型的泊松括号，它与微分拓扑环面和膜代数上的特殊李结构有关，推广了Novikov Balinsky和Gelfand Dorfman以前的研究。详细讨论了李代数和Balinsky—Novikov代数的例证。深入描述了与李代数和Balinsky—Novikov代数有关的交换代数的非结合结构（由导子和自同态诱导）。

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Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators

Abstract We study algebraic properties of Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Special attention is paid to the Poisson brackets of the Lie-Poisson type, related with the special Lie-structures on the differential-topological torus and brane algebras, generalizing those studied before by Novikov-Balinsky and Gelfand-Dorfman. Illustrative examples of Lie and Balinsky-Novikov algebras are discussed in detail. The non-associative structures (induced by derivation and endomorphism) of commutative algebras related to Lie and Balinsky-Novikov algebras are described in depth.

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来源期刊

Topological Algebra and its Applications Mathematics-Algebra and Number Theory

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

24 weeks