##### Department of Mathematics,

University of California San Diego

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### Math 211A: Seminar in Algebra

## Dr. Lucas Buzaglo

#### UC San Diego

## Universal enveloping algebras of infinite-dimensional Lie algebras

##### Abstract:

Universal enveloping algebras of finite-dimensional Lie algebras are fundamental examples of well-behaved noncommutative rings. On the other hand, enveloping algebras of infinite-dimensional Lie algebras remain mysterious. For example, it is widely believed that they are never noetherian, but there are very few examples whose noetherianity is known. In this talk, I will summarize what is known about the noetherianity of enveloping algebras, with a focus on Lie algebras of derivations of associative algebras.

Dan Rogalski, Alireza Golsefidy

### November 4, 2024

### 3:00 PM

APM 7321

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