SOME RESULTS ON LIE COLOR TRIPLE SYSTEMS
In this paper, we establish a close relationship between Lie color triple systems and Lie supertriple systems. Also, we study the connection between Lie color triple systems and involutions of Lie color algebras.
Lie color algebra, involution, –1-eigenspace.
Received: November 17, 2022; Accepted: December 24, 2022; Published: January 10, 2023
How to cite this article: Sibiri Kabore and Patricia L. Zoungrana, Some results on Lie color triple systems, JP Journal of Geometry and Topology 29(1) (2023), 1-17. http://dx.doi.org/10.17654/0972415X23001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] Dongho Moon, The centralizer algebras of Lie color algebras, J. Communications in Algebra 27(7) (1999), 3233-3261.[2] E. Cartan, œuvre complètes, Part 1, Vol. 2, Nos. 107, 138, Paris, Gauthier-Vollars, 1952.[3] T. L. Hodge, Lie triple systems, restricted Lie triple systems and algebraic groups, J. Algebra 244 (2001), 533-580.[4] P. L. Zoungrana, A note on Lie-Yamaguti superalgebras, Far East J. Math. Sci. (FJMS) 100(1) (2016), 1-18.[5] Martín Antonio J. Calderón and José M. Sánchez Delgado, On the structure of split Lie color algebras, Linear Algebra and its Applications 436(2) (2012), 307-315.[6] Meyer Philippe, Representation Associated to Gradations of Lie Algebras and Colour Lie Algebras, Diss. Université de Strasbourg, 2019.[7] N. Bourbaki, Algèbre Chap. II, Harmann, Paris, 1962.[8] N. Bourbaki, Algèbre Chap. III, Harmann, Paris, 1971.[9] R. Ree, Generalized Lie elements, Canadian J. Math. Phys. 12 (1960), 493-502.[10] Manfred Scheunert, Generalized Lie algebras, Journal of Mathematical Physics 4(20) (1979), 712-720.[11] A. N. Issa and P. L. Zoungrana, On Lie-Yamaguti color algebras, Mat. Vesnik 71(3) (2019), 196-206.[12] Yan Cao, Jian Zhang and Yunan Cui, On split Lie color triple systems, J. Open Mathematics 17 (2019), 267-281.[13] Zhang Zhixue, Liu Wenli and Jia Peipei, On the classification of simple Lie supertriple systems, J. Advances in Mathematics 40(3) (2011), 293-298.[14] Zoungrana Patricia Lucie and Pilabre, Nakelgbamba Boukary, On Lie superalgebras involutions and Lie supertriple systems, International Journal of Mathematical Sciences and Applications 4(1) (2014), 53-71.