##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Pavel Kolesnikov

#### Russian Academy of Sciences / UCSD

## Faithful representations of finite Lie conformal algebras

##### Abstract:

Conformal algebras appeared initially in the theory of vertex operator as an algebraic language describing the properties of the singular part of the operator product expansion (OPE). On the other hand, {\em finite} conformal algebras provide a natural approach to the study of certain infinite-dimensional algebras in which the multiplication table is given by a finite number of algebraic functions. In this talk, we study the natural relation between associative and Lie conformal algebras. Every associative conformal algebra can be turned into a Lie conformal algebra in the ordinary way. But it is still unknown whether a finite Lie conformal algebra can be embedded into an appropriate associative conformal algebra. A finer problem also makes sense: Whether a finite Lie conformal algebra has a faithful finite representation? We prove that if a finite Lie conformal algebra admits Levi decomposition then it has a finite faithful representation.

Host: Efim Zelmanov

### February 26, 2013

### 2:00 PM

### AP&M 7218

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