3-李-Rinehart Color代数的上同调与形变

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (1): 35-0043.

3-李-Rinehart Color代数的上同调与形变

腾文^1,2, 游泰杰¹

1. 贵州师范大学数学科学学院, 贵阳 550025; 2. 贵州财经大学数统学院, 贵阳 550025

收稿日期:2021-03-25 出版日期:2022-01-26 发布日期:2022-01-26
通讯作者: 游泰杰 E-mail: youtaijie@126.com

Cohomology and Deformations of 3-Lie-Rinehart Color Algebras

TENG Wen^1,2, YOU Taijie¹

1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China;
2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Received:2021-03-25 Online:2022-01-26 Published:2022-01-26

摘要/Abstract

摘要： 首先, 通过引入3-李-Rinehart color代数的概念, 利用3-李-Rinehart color代数的表示讨论其上同调；其次, 给出3-李-Rinehart color代数的1-余循环和2-余循环之间的关系; 最后, 作为应用, 通过上同调理论刻画其形变.

关键词: 3-李-Rinehart color代数, 上同调, 形变

Abstract: Firstly, by introducing the concept of 3-Lie-Rinehart color algebra and using the representation of 3-Lie-Rinehart color algebras, we
discussed its cohomology. Secondly, we gave relationship between 1-cocycle and 2-cocycle of 3-Lie-Rinehart color algebras. Finally, as an application, we characterized the deformations of 3-Lie-Rinehart color algebras by the cohomology theory.

Key words: 3-Lie-Rinehart color algebra, cohomology, deformation

中图分类号:

O152.5

腾文, 游泰杰. 3-李-Rinehart Color代数的上同调与形变[J]. 吉林大学学报(理学版), 2022, 60(1): 35-0043.

TENG Wen, YOU Taijie. Cohomology and Deformations of 3-Lie-Rinehart Color Algebras[J]. Journal of Jilin University Science Edition, 2022, 60(1): 35-0043.

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