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arXiv · 1601.07570

Bimodule Structure of Central Simple Algebras

Eliyahu Matzri·Louis H. Rowen·David J Saltman·Uzi Vishne
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Abstract

For a maximal separable subfield $K$ of a central simple algebra $A$, we provide a semiring isomorphism between $K$-$K$-bimodules $A$ and $H$-$H$ bisets of $G = \Gal(L/F)$, where $F = \operatorname{Z}(A)$, $L$ is the Galois closure of $K/F$, and $H = \Gal(L/K)$. This leads to a combinatorial interpretation of the growth of $\dim_K((KaK)^i)$, for fixed $a \in A$, especially in terms of Kummer sets.

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Eliyahu Matzri, Louis H. Rowen, David J Saltman, Uzi Vishne. 2016-01-27. Bimodule Structure of Central Simple Algebras. https://arxiv.org/abs/1601.07570

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