A-扩张Lie Rinehart代数

数学季刊 ›› 2007, Vol. 22 ›› Issue (3): 317-327.

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A-扩张Lie Rinehart代数

1. School of Mathematical Sciences and LMAM Peking University 2. Department of Mathematics Qinghai Normal University

收稿日期:2005-06-20 出版日期:2007-09-30 发布日期:2023-10-25
作者简介:CHEN Zhuo(1971-), male, native of Xi'an, Shannxi, a lecturer of Peking University, Ph.D., engages in Poisson geometry; QI Yu-hai(1968-), female(Tuzu), native of Xining, Qinghai, an associate professor of Qinghai Normal University, M.S.D., engages in mathematical physics.
基金资助:
Supported by the China Postdoctoral Science Foundation(20060400017)

On the A-extended Lie Rinehart Algebras

1. School of Mathematical Sciences and LMAM Peking University 2. Department of Mathematics Qinghai Normal University

Received:2005-06-20 Online:2007-09-30 Published:2023-10-25
About author:CHEN Zhuo(1971-), male, native of Xi'an, Shannxi, a lecturer of Peking University, Ph.D., engages in Poisson geometry; QI Yu-hai(1968-), female(Tuzu), native of Xining, Qinghai, an associate professor of Qinghai Normal University, M.S.D., engages in mathematical physics.
Supported by:
Supported by the China Postdoctoral Science Foundation(20060400017)

摘要/Abstract

摘要： The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.

关键词: Lie Rinehart algebra, A-extended algebra, action algebra, Lie group, Lie algebra

Abstract: The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.

Key words: Lie Rinehart algebra, A-extended algebra, action algebra, Lie group, Lie algebra

中图分类号:

O153

陈酌, 祁玉海. A-扩张Lie Rinehart代数[J]. 数学季刊, 2007, 22(3): 317-327.

CHEN Zhuo, QI Yu-hai. On the A-extended Lie Rinehart Algebras [J]. Chinese Quarterly Journal of Mathematics, 2007, 22(3): 317-327.

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A-扩张Lie Rinehart代数

On the A-extended Lie Rinehart Algebras

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