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Axioms 2017, 6(4), 33; doi:10.3390/axioms6040033

Universal Enveloping Commutative Rota–Baxter Algebras of Pre- and Post-Commutative Algebras

1
Laboratory of Rings Theory, Sobolev Institute of Mathematics of the SB RAS, Acad. Koptyug ave., 4, 630090 Novosibirsk, Russia
2
Department of Mathematics and Mechanics, Novosibirsk State University, Pirogova str., 2, 630090 Novosibirsk, Russia
Received: 2 October 2017 / Revised: 22 November 2017 / Accepted: 4 December 2017 / Published: 7 December 2017
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)
View Full-Text   |   Download PDF [275 KB, uploaded 7 December 2017]

Abstract

Universal enveloping commutative Rota–Baxter algebras of pre- and post-commutative algebras are constructed. The pair of varieties (RBλCom, postCom) is proved to be a Poincaré–Birkhoff–Witt-pair (PBW)-pair and the pair (RBCom, preCom) is proven not to be. View Full-Text
Keywords: Rota–Baxter algebra; universal enveloping algebra; PBW-pair of varieties; Zinbiel algebra; dendriform algebra; pre-commutative algebra; post-commutative algebra Rota–Baxter algebra; universal enveloping algebra; PBW-pair of varieties; Zinbiel algebra; dendriform algebra; pre-commutative algebra; post-commutative algebra
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gubarev, V. Universal Enveloping Commutative Rota–Baxter Algebras of Pre- and Post-Commutative Algebras. Axioms 2017, 6, 33.

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