Functorial PBW theorems for post-Lie algebras

Abstract

Using the categorical approach to Poincaré-Birkhoff-Witt type theorems from our previous work with Tamaroff, we prove three such theorems: for universal enveloping Rota-Baxter algebras of tridendriform algebras, for universal enveloping Rota--Baxter Lie algebras of post-Lie algebras, and for universal enveloping tridendriform algebras of post-Lie algebras. Similar results, though without functoriality of the PBW isomorphisms, were recently obtained by Gubarev. Our methods are completely different and mainly rely on methods of rewriting theory for shuffle operads.

8 pages, comments are welcome

References in corpus (3)

• Loday-type Algebras and the Rota-Baxter Relation
• Algebraic structures of $F$-manifolds via pre-Lie algebras
• Universal enveloping Rota-Baxter algebras of preassociative and postassociative algebras

Cited by in corpus (2)

• Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
• Endofunctors and Poincaré-Birkhoff-Witt theorems