PBW Property for Associative Universal Enveloping Algebras over an Operad

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Abstract

Given a symmetric operad P and a P-Algebra V, the associative universal enveloping algebra UP is an associative algebra whose category of modules is isomorphic to the abelian category of V-modules. We study the notion of PBW property for universal enveloping algebras over an operad. In case P is Koszul a criterion for the PBW property is found. A necessary condition on the Hilbert series for P is discovered. Moreover, given any symmetric operad P, together with a Gröbner basis G, a condition is given in terms of the structure of the underlying trees associated with leading monomials of G, sufficient for the PBW property to hold. Examples are provided.

Original languageAmerican English
Pages (from-to)3106-3143
Number of pages38
JournalInternational Mathematics Research Notices
Volume2022
Issue number4
DOIs
StatePublished - 1 Feb 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

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