##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Robert Won

#### UCSD

## The graded module category of a generalized Weyl algebra

##### Abstract:

The first Weyl algebra $A = k\langle x,y \rangle/(xy - yx - 1)$ is a well-studied noncommutative $\mathbb {Z}$-graded ring. Generalized Weyl algebras, introduced by Bavula, are a class of noncommutative $\mathbb {Z}$-graded rings which generalize the Weyl algebra. In this talk, we investigate the category of graded modules over certain generalized Weyl algebras and construct commutative rings with equivalent graded module categories. Along the way, we will learn about graded rings, noncommutative projective schemes, and how to do geometry without a geometric space.

Advisor: Daniel Rogalski

### May 2, 2016

### 4:00 PM

### AP&M 6402

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