The center of the generic algebra of degree p

Esther Beneish

paper

The center of the generic algebra of degree p

arXiv:0704.3450

Abstract

Let $F$ be an algebraically closed field of characteristic zero, and let $p$ be an odd prime. We show that the center of the generic division algebra of degree $p$ is stably rational over $F$ . Equivalently, if we let $V = M_{p} (F) \oplus M_{p} (F)$ and $P G L_{p}$ act on $V$ by simultaneous conjugation, then we show that the function field of the quotient variety $V / P G L_{p}$ is stably rational over $F$ .

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