Universal enveloping Rota-Baxter algebras of preassociative and postassociative algebras

Abstract

Universal enveloping Rota-Baxter algebras of preassociative and postassociative algebras are constructed. The question of Li Guo is answered: the pair of varieties (Rota-Baxter algebras of nonzero weight,postassociative algebras) is a PBW-pair and the pair (Rota-Baxter algebras of zero weight,preassociative algebras) is not.

27 pages

References in corpus (4)

• Loday-type Algebras and the Rota-Baxter Relation
• Mixable Shuffles, Quasi-shuffles and Hopf Algebras
• Operads of decorated trees and their duals
• Groebner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra

Cited by in corpus (4)

• Functorial PBW theorems for post-Lie algebras
• Universal enveloping Lie Rota-Baxter algebra of preLie and post-Lie algebras
• Commutative post-Lie algebra structures on Kac--Moody algebras
• Universal enveloping commutative Rota-Baxter algebras of precommutative and postcommutative algebras