A Lie algebraic approach to Novikov algebras

被引：17

作者：

Bai, CM ^{[1
]}

Meng, DJ

机构：

[1] Nankai Inst Math, Div Theoret Phys, Tianjin 300071, Peoples R China

[2] Nankai Inst Math, Dept Math, Tianjin 300071, Peoples R China

[3] Liu Hui Ctr Appl Math, Tianjin 300071, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2003年 / 45卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Novikov algebras; Novikov interior derivation algebras; linear deformation;

D O I：

10.1016/S0393-0440(02)00150-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Novikov algebras were introduced in connection with Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. The commutator of a Novikov algebra is a Lie algebra. Thus it is useful to relate the study of Novikov algebras to the theory of Lie algebras. In this paper, we will try to realize Novikov algebras through a Lie algebraic approach. Such a realization could be important in physics and geometry. We find that all transitive Novikov algebras in dimension less than or equal to3 can be realized as the Novikov algebras obtained through Lie algebras and their compatible linear (global) deformations. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：218 / 230

页数：13

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