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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (2): 32-37,46.doi: 10.6040/j.issn.1671-9352.0.2022.665

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微分Lie-Yamaguti超代数的上同调与形变

腾文(),龙凤山   

  1. 贵州财经大学数学与统计学院, 贵州 贵阳 550025
  • 收稿日期:2022-12-16 出版日期:2024-02-20 发布日期:2024-02-20
  • 作者简介:腾文(1986—)，男，讲师，博士，研究方向为代数学及其应用. E-mail: tengwen@mail.gufe.edu.cn
  • 基金资助:
    贵州省科技计划项目(黔科合基础[2018]1020);贵州省高等学校系统建模与数据挖掘重点实验室项目(2023013);贵州省科技厅基金项目(黔科合基础-ZK[2023]一般025)

Cohomology and deformation of differential Lie-Yamaguti superalgebras

Wen TENG(),Fengshan LONG   

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China
  • Received:2022-12-16 Online:2024-02-20 Published:2024-02-20

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摘要：

给出微分Lie-Yamaguti超代数的表示和上同调，并根据上同调考虑微分Lie-Yamaguti超代数的线性形变。

关键词: 微分Lie-Yamaguti超代数, 上同调, 线性形变

Abstract:

Firstly, the representation and cohomology of differential Lie-Yamaguti superalgebras are introduced. Then, the linear deformation of differential Lie-Yamaguti superalgebras is considered according to cohomology.

Key words: differential Lie-Yamaguti superalgebra, cohomology, linear deformation

中图分类号: 

  • O152.5
1 KINYON M K , WEINSTEIN A . Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces[J]. American Journal of Mathematics, 2001, 123 (3): 525- 550.
doi: 10.1353/ajm.2001.0017
2 NOMIZU K . Invariant affine connections on homogeneous spaces[J]. American Journal of Mathematics, 1954, 76 (1): 33- 65.
doi: 10.2307/2372398
3 YAMAGUTI K . On the Lie triple system and its generalization[J]. Journal of Science of the Hiroshima University, Series A, 1958, 21 (3): 155- 160.
4 YAMAGUTI K . On cohmology groups of general Lie triple systems[J]. Kumamoto Journal of Science, Series A, 1969, 8 (4): 135- 146.
5 ZOUNGRANA P L . A note on Lie-Yamaguti superalgebras[J]. Far East Journal of Mathematical Sciences, 2016, 100 (1): 1- 18.
6 ZOUNGRANA P L , ISSA A N . On Killing forms and invariant forms of Lie-Yamaguti superalgebras[J]. International Journal of Mathematics and Mathematical Sciences, 2017, 2017 (1): 1- 9.
7 唐鑫鑫, 胡梦如, 徐建国, 等. Lie-Yamaguti超代数的交换扩张[J]. 东北师大学报(自然科学版), 2018, 50 (4): 1- 5.
TANG Xinxin , HU Mengru , XU Jianguo , et al. Abelian extensions of Lie-Yamaguti superalgebras[J]. Journal of Northeast Normal University(Natural Science Edition), 2018, 50 (4): 1- 5.
8 TANG Xinxin , ZHANG Qingcheng , WANG Chunyue . From Leibniz superalgebras to Lie-Yamaguti superalgebras[J]. Journal of Mathematics, 2018, 38 (4): 589- 601.
9 VORONOV T . Higher derived brackets and homotopy algebras[J]. Journal of Pure and Applied Algebra, 2005, 202 (1/2/3): 133- 153.
10 COLL V , GERSTENHABER M , GIAQUINTO A . An explicit deformation formula with noncommuting derivations[M]. Weizmann: Jerusalem, 1989.
11 MAGID A . Lectures on differential Galois theory[M]. Providence, RI: American Mathematical Society, 1994.
12 RACHUNEK J , ŠALOUNOVA D . Derivations on algebras of a non-commutative generalization of the Łukasiewicz logic[J]. Fuzzy Sets and Systems, 2018, 333, 11- 16.
13 LODAY J L . On the operad of associative algebras with derivation[J]. Georgian Mathematical Journal, 2010, 17 (2): 347- 372.
14 TANG R , FRÉGIER Y , SHENG Y H . Cohomologies of a Lie algebra with a derivation and applications[J]. Journal of Algebra, 2019, 534 (3): 65- 99.
15 WU Xueru , MA Yao , CHEN Liangyun . Abelian extensions of Lie triple systems with derivations[J]. Electronic Research Archive, 2022, 30 (3): 1087- 1103.
doi: 10.3934/era.2022058
16 GUO Shuangjian . Central extensions and deformations of Lie triple systems with a derivation[J]. Journal of Mathematical Research with Applications, 2022, 42 (2): 189- 198.
17 ZHAO Xiaodong, CHEN Liangyun. Cohomologies and deformations of Lie superalgebras with superderivations[EB/OL]. (2021-10-27)[2022-12-10].https://www.researchgate.net/publication/355675478.
18 郭双建. 具有导子的 Lie-Yamaguti 代数[J]. 数学学报(中文版), 2023, 66 (3): 547- 556.
19 TENG Wen , YOU Taijie . Derivations and deformations of Lie-Yamaguti color algebras[J]. Journal of Mathematical Research with Applications, 2022, 42 (1): 15- 30.
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