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arXiv · 0704.3450

The center of the generic algebra of degree p

Esther Beneish
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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 $PGL_p$ act on $V$ by simultaneous conjugation, then we show that the function field of the quotient variety $V/PGL_p$ is stably rational over $F$.

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Esther Beneish. 2012-03-26. The center of the generic algebra of degree p. https://arxiv.org/abs/0704.3450

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