PBW property for associative universal enveloping algebras over an operad [article]

Anton Khoroshkin
2020 arXiv   pre-print
Given a symmetric operad P and a P-algebra V, the associative universal enveloping algebra U_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 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
more » ... 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.
arXiv:1807.05873v3 fatcat:gms4bp43xnhb7km773bq42vztu