##### Department of Mathematics,

University of California San Diego

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### Algebra

## Jack Sonn

#### Technion, Haifa, Israel

## The projective Schur subgroup of the Brauer group

##### Abstract:

A noncommutative analogue of a cyclotomic field extension in the realm of central simple algebras is a Schur algebra, namely a finite dimensional central simple algebra $A$ over a field $K$ which is generated over $K$ by a finite subgroup of the multiplicative group of $A$. Its projective version, a projective Schur algebra, is the noncommutative analogue of a radical field extension, namely a finite dimensional central simple algebra $A$ over a field $K$ which is generated over $K$ by a subgroup $G$ of the multiplicative group of $A$ such that $G/K*$ is finite. The talk will focus on projective Schur algebras and the subgroup of the Brauer group that they determine.

Host: Adrian Wadsworth

### January 10, 2005

### 2:00 PM

### AP&M 6438

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