Geodesic
Universal Enveloping Algebras and Poincaré-Birkhoff-Witt Theorem for Involutive Hom-Lie Algebras
Journal of Lie theory, Tome 28 (2018) no. 3, pp. 735-756
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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.
Classification : 17A30,17A50,17B35
Mots-clés : Hom-Lie algebra, Hom-associative algebra, involution, universal enveloping algebra, Poincaré-Birkhoff-Witt theorem 
@article{JLT_2018_28_3_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a7/}
}
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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, Tome 28 (2018) no. 3, pp. 735-756. http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a7/