Bimodule Structure of Central Simple Algebras

الأصل · EN

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 = (L/F), where F = Z(A), L is the Galois closure of K/F, and H = (L/K). This leads to a combinatorial interpretation of the growth of ₖ((KaK)ⁱ), for fixed a ∈ A, especially in terms of Kummer sets.