We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
PBW Property for Associative Universal Enveloping Algebras Over an Operad.
- Authors
Khoroshkin, Anton
- Abstract
Given a symmetric operad |$\mathcal{P}$| and a |$\mathcal{P}$| -algebra |$V$| , the associative universal enveloping algebra |${\textsf{U}_{\mathcal{P}}}$| 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 |$\mathcal{P}$| is Koszul a criterion for the PBW property is found. A necessary condition on the Hilbert series for |$\mathcal{P}$| is discovered. Moreover, given any symmetric operad |$\mathcal{P}$| , 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.
- Subjects
UNIVERSAL algebra; GROBNER bases; ABELIAN categories; NONASSOCIATIVE algebras; HILBERT algebras
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 4, p3106
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnaa215