##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Jason Gaddis

#### UCSD

## Two-parameter analogs of the Heisenberg enveloping algebra

##### Abstract:

The harmonic oscillator problem in quantum mechanics is to find operators $a$ and $b$ acting on a Hilbert space satisfying the relation $ab-ba=1$. This is one of the physical motivations behind studying the Weylalgebra and the enveloping algebra of the Heisenberg Lie algebra. In this talk, I will present a two-parameter version of this problem and discuss some of the subtleties in looking for simple, primitive factor rings in quantum enveloping algebras.

### October 28, 2013

### 3:00 PM

### AP&M 7218

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