##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Sue Sierra

#### University of Michigan

## Rings graded equivalent to the Weyl algebra

##### Abstract:

Let $A$ be the first Weyl algebra, in the Euler gradation. We classify graded rings $B$ such that $gr-A$ and $gr-B$ are equivalent (we say that $A$ and $B$ are graded equivalent), and produce some surprising examples. In particular, we show that $A$ is graded equivalent to an idealizer in a localization of $A$. In the process, we derive a concise new characterization of equivalences of graded module categories that generalizes the classical Morita theorems.

Hosts: Dan Rogalski and Lance Small

### December 5, 2007

### 1:00 PM

### AP&M 7218

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