Journal of Lie Theory

no. 3
Universal Enveloping Algebras and Poincaré-Birkhoff-Witt Theorem for Involutive Hom-Lie Algebras
Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 735-756
Hom-type algebras, in particular Hom-Lie algebras, have attracted quite much attention in recent years. A Hom-Lie algebra is called involutive if its Hom map is multiplicative and involutive. In this paper, we obtain an explicit construction of the free involutive Hom-associative algebra on a Hom-module. We then apply this construction to obtain the universal enveloping algebra of an involutive Hom-Lie algebra. Finally we generalize the well-known Poincaré-Birkhoff-Witt theorem for enveloping algebras of Lie algebras to involutive Hom-Lie algebras.
DOI: 10.5802/jolt.1023
Classification: 17A30,17A50,17B35
Keywords: Hom-Lie algebra, Hom-associative algebra, involution, universal enveloping algebra, Poincaré-Birkhoff-Witt theorem 
@article{JOLT_2018_28_3_a7,
     author = {L. Guo and B. Zhang and S. Zheng},
     title = {Universal {Enveloping} {Algebras} and {Poincar\'e-Birkhoff-Witt} {Theorem} for {Involutive} {Hom-Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {735--756},
     year = {2018},
     volume = {28},
     number = {3},
     doi = {10.5802/jolt.1023},
     zbl = {1422.17001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1023/}
}
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JO  - Journal of Lie Theory
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%A B. Zhang
%A S. Zheng
%T Universal Enveloping Algebras and Poincaré-Birkhoff-Witt Theorem for Involutive Hom-Lie Algebras
%J Journal of Lie Theory
%D 2018
%P 735-756
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L. Guo; B. Zhang; S. Zheng. Universal Enveloping Algebras and Poincaré-Birkhoff-Witt Theorem for Involutive Hom-Lie Algebras. Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 735-756. doi: 10.5802/jolt.1023

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