# On the PBW property for universal enveloping algebras

`2023-03-29 10:30:00``2023-03-29 11:30:00``On the PBW property for universal enveloping algebras``The famous Poincaré-Birkhoff-Witt theorem states that there is a canonical filtration on the universal enveloping algebra of any Lie algebra such that the associated graded algebra is isomorphic to a symmetric algebra of the underlying space. I will explain what one can say about the PBW property for different algebraic structures, such as pre-Lie algebras, Poisson algebras, algebras admitting a pair of compatible Lie brackets, and many others. Moreover, I will explain a necessary and sufficient condition for the PBW property using the language of (colored) operads and Gröbner basis machinery. All necessary definitions will be recalled during the talk. ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062``Third floor seminar room, Mathematics building, and on Zoom. See link below.``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`The famous Poincaré-Birkhoff-Witt theorem states that there is a canonical filtration on the universal enveloping algebra of any Lie algebra such that the associated graded algebra is isomorphic to a symmetric algebra of the underlying space. I will explain what one can say about the PBW property for different algebraic structures, such as pre-Lie algebras, Poisson algebras, algebras admitting a pair of compatible Lie brackets, and many others.

Moreover, I will explain a necessary and sufficient condition for the PBW property using the language of (colored) operads and Gröbner basis machinery.

All necessary definitions will be recalled during the talk.

================================================

https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 22/03/2023