On the PBW property for universal enveloping algebras

Seminar
Algebra
Speaker
Anton Khoroshkin (Haifa University)
Date
29/03/2023 - 11:30 - 10:30Add to Calendar 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
Place
Third floor seminar room, Mathematics building, and on Zoom. See link below.
Abstract

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. 

 

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

Meeting ID: 878 5613 2062

Last Updated Date : 22/03/2023