Deformations and extensions of modified <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mi mathvariant="bold-italic">λ</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/2C98644B-F259-436a-9135-6B37309AF158-M001.jpg"><?fx-imagestate width="3.55599999" height="3.97933316"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/2C98644B-F259-436a-9135-6B37309AF158-M001c.jpg"><?fx-imagestate width="3.55599999" height="3.97933316"?></graphic></alternatives></inline-formula>-differential Lie-Yamaguti algebras

TENG Wen; PAN Yuewei

doi:10.13471/j.cnki.acta.snus.ZR20240283

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Deformations and extensions of modified

λ

-differential Lie-Yamaguti algebras

Research articles | 更新时间：2025-11-14

- Deformations and extensions of modified $λ$ -differential Lie-Yamaguti algebras
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 4, Pages: 115-127(2025)
- 作者机构：
  
  1.贵州财经大学数学与统计学院，贵州贵阳 550025
  2.贵州商学院计算机与信息工程学院，贵州贵阳 550014
- 作者简介：
  
  TENG Wen（tengwen@mail.gufe.edu.cn）
  PAN Yuewei（yueweiPanGZSD@163.com）
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240283
  CLC： O152.5
- Received：16 September 2024，
  
  Accepted：24 January 2025，
  
  Published Online：03 June 2025，
  
  Published：25 July 2025
- 稿件说明：
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腾文,潘越伟.修正λ-微分Lie-Yamaguti代数的形变和扩张[J].中山大学学报(自然科学版)(中英文),2025,64(04):115-127.

TENG Wen,PAN Yuewei.Deformations and extensions of modified λ-differential Lie-Yamaguti algebras[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(04):115-127.
腾文,潘越伟.修正λ-微分Lie-Yamaguti代数的形变和扩张[J].中山大学学报(自然科学版)(中英文),2025,64(04):115-127. DOI： 10.13471/j.cnki.acta.snus.ZR20240283.

TENG Wen,PAN Yuewei.Deformations and extensions of modified λ-differential Lie-Yamaguti algebras[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(04):115-127. DOI： 10.13471/j.cnki.acta.snus.ZR20240283.

Deformations and extensions of modified

λ

-differential Lie-Yamaguti algebras

PDF Download

摘要

考虑了修正

-微分Lie-Yamaguti代数，其由一个Lie-Yamaguti代数和一个修正

-微分算子组成. 首先我们引入修正

-微分Lie-Yamaguti代数的表示. 此外，我们建立了系数在表示中的修正

-微分Lie-Yamaguti代数的上同调. 最后，我们利用第二上同调群研究了修正

-微分Lie-Yamaguti代数的单参数形式变形和Abelian扩张.

Abstract

The modified

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-differential Lie-Yamaguti algebras are considered

in which a modified

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-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modified

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2.62466669

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-differential operator. First we introduce the representation of modified

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-differential Lie-Yamaguti algebras. Furthermore

we establish the cohomology of a modified

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-differential Lie-Yamaguti algebra with coefficients in a representation. Finally

we investigate the one-parameter formal deformations and Abelian extensions of modified

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-differential Lie-Yamaguti algebras using the second cohomology group.

关键词

Keywords

references

BENITO P ， DRAPER C ， ELDUQUE A ， 2005 . Lie-Yamaguti algebra related to <math id="M545"><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836175&type= 3.80999994 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836136&type= 2.62466669 ［J］. J Pure Appl Algebra ， 202 （ 1/2/3 ）： 22 - 54 .

BENITO P ， ELDUQUE A ， MARTÍN-HERCE F ， 2009 . Irreducible Lie-Yamaguti algebras ［J］. J Pure Appl Algebra ， 213 （ 5 ）： 795 - 808 .

GUO L ， KEIGHER W ， 2008 . On differential Rota-Baxter algebras ［J］. J Pure Appl Algebra ， 212 （ 3 ）： 522 - 540 .

GUO S J ， 2023 . Lie-Yamaguti algebras with a derivation ［J］. Acta Math Sin （Chin Ser）， 66 （ 3 ）： 547 - 556 .

GUO S J ， ZHAO J Z ， 2024 . Cohomology of Lie-Yamaguti algebras with higher derivations ［J］. J Guizhou Normal Uni （Natural Sci）， 42 （ 3 ）： 9 - 15+25 .

JIANG J ， SHENG Y H ， 2024 . Deformations of modified <math id="M546"><mi>r</mi></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836162&type= 2.28600001 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836138&type= 1.10066664 -matrices and cohomologies of related algebraic structures ［J］. J Noncommut Geom ， 19 （ 2 ）： 429 - 450 .

KINYON M K ， WEINSTEIN A ， 2001 . Leibniz algebras， courant algebroids and multiplications on reductive homogeneous spaces ［J］. Amer J Math ， 123 （ 3 ）： 525 - 550 .

LIN J ， CHEN L Y ， MA Y ， 2015 . On the deformation of Lie-Yamaguti algebras ［J］. Acta Math Sin （Engl Ser）， 31 （ 6 ）： 938 - 946 .

LONG F S ， TENG W ， 2024 . Representations， cohomologies and abelian extensions of modified <math id="M547"><mi>λ</mi></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836163&type= 2.28600001 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836155&type= 1.94733346 -differential Hom-Lie triple systems ［J］. J Guizhou Normal Univ（Natural Sci）， 42 （ 3 ）： 91 - 96+121 .

NOMIZU K ， 1954 . Invariant affine connections on homogeneous spaces ［J］. Amer J Math ， 76 （ 1 ）： 33 - 65 .

PENG X S ， ZHANG Y ， GAO X ， et al ， 2022 . Universal enveloping of （modified） <math id="M548"><mi>λ</mi></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836163&type= 2.28600001 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84836155&type= 1.94733346 -differential Lie algebras ［J］. Linear Multilinear Algebra ， 70 （ 6 ）： 1102 - 1127 .

SEMENOV-TYAN-SHANSKII M A ， 1983 . What is a classical r-matrix？［J］. Funct Anal Appl ， 17 （ 4 ）： 259 - 272 .

TENG W ， 2024 . Relative differential operators on Lie-Yamaguti algebras ［J］. Chin Annals Math Ser A ， 45 （ 1 ）： 39 - 52 .

YAMAGUTI K ， 1958 . On the Lie triple system and its generalization ［J］. J Sci Hiroshima Univ ， 21 （ 3 ）： 155 - 160 .

YAMAGUTI K ， 1967 . On cohmology groups of general Lie triple systems ［J］. Kumamoto J Sci A ， 8 ： 135 - 146 .

ZHANG T ， LI J ， 2015 . Deformations and extensions of Lie-Yamaguti algebras ［J］. Linear Multilinear Algebra ， 63 （ 11 ）： 2212 - 2231 .

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Deformations and extensions of modified λ-differential Lie-Yamaguti algebras

DOI：10.13471/j.cnki.acta.snus.ZR20240283

摘要

Abstract

关键词

Keywords

references

Deformations and extensions of modified $λ$ -differential Lie-Yamaguti algebras