##### Department of Mathematics,

University of California San Diego

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### University of California Lie Theory Workshop

## Susan Montgomery

#### University of Southern California

## Orthogonal Representations of Hopf Algebras

##### Abstract:

Let H be a Hopf algebra over an algebraically closed field of characteristic not 2. Assume that the antipode of H has period 2, and let V be a finite-dimensional representation of H. Then if V is self-dual, it must be either ``orthogonal'' or ``symplectic'' , in the sense that it admits a non-degenerate H-invariant bilinear form which is either symmetric or skew-symmetric. We consider various Hopf algebras constructed from finite groups, and investigate when all of their (fin dim) representations are orthogonal in the above sense.

Host: Efim Zelmanov

### February 16, 2008

### 8:00 AM

### NSB 1205

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