Graduate Student Seminar

Seminars in this series are for students to talk about something of  personal interest, or a professor to describe and explore their area of research.

The talks are at a very accessible level.

Free pizzas are a regular part  of this seminar series.

Further information on seminars can be found at the following link: http://www.math.toronto.edu/mgsa/seminar

Details

Enveloping algebras of nonassociative structures

by Marina Tvalavadze | Fields Institute
Time: 13:10  (Thursday, Mar. 29, 2012)
Location: BA6183, Bahen Center, 40 St. George St.
Abstract:
Nonassociative algebras are very rich in algebraic structure. They have important applications not only in many branches of mathematics but also in physics. Perhaps, a Lie algebra is the most known example of a nonassociative algebra. In the classical theory of Lie algebras, the famous Poincar\'e-Birkhoff-Witt (PBW) theorem (Poincar\'e (1900), G. D. Birkhoff (1937), Witt (1937)) establishes a fundamental connection between Lie and associative algebras by relating the universal associative enveloping algebra to any Lie algebra $L$. Since then the analogous results for other nonassociative structures such as generalized Lie algebras, Leibnitz $n$-algebras, triple systems, etc. have been discovered. This allowed to describe their representations by means of universal enveloping algebras and to make calculations in a similar way as in a ring of polynomials $F[x_1,\ldots,x_n]$. The aim of this talk is to discuss some classical as well as recent (including the speaker's) results on the universal enveloping algebras for different types of algebras.

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· Wednesday, Mar. 17, 2010: The Planar Dimer Model, continued (Alex Bloemendal)
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· Thursday, Nov. 18, 2010: A short introduction to curve singularities (Dmitry Kerner)
· Thursday, Nov. 25, 2010: Newton diagrams and applications (Dmitry Kerner)
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