JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 6-12.doi: 10.6040/j.issn.1671-9352.0.2022.010

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Pre-Lie-Yamaguti color algebra and color O-operator

TENG Wen1,2, YOU Tai-jie2*   

  1. 1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China;
    2. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2023-02-12

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Abstract: The definition of pre-Lie-Yamaguti color algebra is introduced. The color O -operator of Lie-Yamaguti color algebra about representation space is given, and its relationship with pre-Lie-Yamaguti color algebra is discussed. It is proved that a pre-Lie-Yamaguti color algebra can induce a Lie-Yamaguti color algebra and a representation on itself.

Key words: Pre-Lie-Yamaguti color algebra, Lie-Yamaguti color algebra, color O-operator, color Rota-Baxter operator

CLC Number: 

  • O152.5
[1] YAMAGUTI K. On the Lie triple system and its generalization[J]. J Sci Hiroshima Univ Ser A, 1957/1958, 21:155-160.
[2] LIN Jie, CHEN Liangyun, MA Yao. On the deformations of Lie-Yamaguti algebras[J]. Acta Math Sin(Engl Ser), 2015, 31(6):938-946.
[3] SHENG Yunhe, ZHAO Jia, ZHOU Yanqiu. Nijenhuis operators, product structures and complex structures on Lie-Yamaguti algebras[J]. J Algebra Appl, 2021, 20(8):1-22.
[4] SHENG Yunhe, ZHAO Jia. Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras[J/OL]. Communications in Algebra, 2022, 50(9):4056-4073.
[5] ZHANG Tao, LI Juan. Deformations and extensions of Lie-Yamaguti algebras[J]. Linear and Multilinear Alg, 2015, 63:2212-2231.
[6] ZOUNGRANA P L. A note on Lie-Yamaguti superalgebras[J]. Far East J Math Sci, 2016, 100(1):1-18,.
[7] ZOUNGRANA P L, ISSA A N. On Killing forms and invariant forms of Lie-Yamaguti superalgebras[J]. Int J Math Math Sci, 2017, 2017: 1-9.
[8] ISSA A N, ZOUNGRANA P L. On Lie-Yamaguti color algebras[J]. Mat Vesnik, 2019, 71(3):196-206.
[9] TENG Wen, YOU Taijie. Derivations and deformations of Lie-Yamaguti color algebras[J]. Journal of Mathematical Research with Applications, 2022, 42(1):15-30.
[10] SCHEUNERT M. Generalized Lie algebras[J]. J Math Phys, 1979, 20(4):712-720.
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