Geodesic
Poincaré-Birkhoff-Witt Theorem for Pre-Lie and Post-Lie Algebras
Vsevolod Gubarev1, 2
1Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
2Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria
Journal of Lie Theory, Tome 30 (2020) no. 1, pp. 223-238

Voir la notice de l'article provenant de la source Heldermann Verlag

We construct the universal enveloping preassociative and postassociative algebra for a pre-Lie and a post-Lie algebra, respectively. We show that the pairs (pre-Lie, pre-As) and (post-Lie, post-As) are Poincaré-Birkhoff-Witt-pairs; for the first this is a reproof of the result of V. Dotsenko and P. Tamaroff.
Classification : 16W99,17D25
Mots-clés : Rota-Baxter operator, Groebner-Shirshov basis, pre-Lie algebra, post-Lie algebra, preassociative algebra, dendriform algebra, postassociative algebra

Vsevolod Gubarev  1 , 2

1 Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
2 Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria 
Vsevolod Gubarev. Poincaré-Birkhoff-Witt Theorem for Pre-Lie and Post-Lie Algebras. Journal of Lie Theory, Tome 30 (2020) no. 1, pp. 223-238. http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a12/
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     author = {Vsevolod Gubarev},
     title = {Poincar\'e-Birkhoff-Witt {Theorem} for {Pre-Lie} and {Post-Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {223--238},
     year = {2020},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a12/}
}
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