Bimodule Structure of Central Simple Algebras

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 $F=Z(A)$, $L$ 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.

Cited by in corpus (1)

• Symbol $p$-Algebras of Prime Degree and their $p$-Central Subspaces