Bimodule structure of central simple algebras

Eliyahu Matzri; Louis H. Rowen; David Saltman; Uzi Vishne

doi:10.1016/j.jalgebra.2016.07.039

Bimodule structure of central simple algebras

Eliyahu Matzri
, Louis H. Rowen
, David Saltman
, Uzi Vishne

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For a maximal separable subfield K of a central simple algebra A, we provide a semiring isomorphism between K–K-sub-bimodules of A and H–H-sub-bisets of G=Gal(L/F), where F=Cent(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∈A, especially in terms of Kummer subspaces.

Original language	English
Pages (from-to)	454-479
Number of pages	26
Journal	Journal of Algebra
Volume	471
DOIs	https://doi.org/10.1016/j.jalgebra.2016.07.039
State	Published - 1 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Funding

This work was supported by the United States-Israel Binational Science Foundation (grant no. 201049 ).

Funders	Funder number
United States-Israel Binational Science Foundation	201049

Keywords

Bimodules
Division algebras
Subfields

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10.1016/j.jalgebra.2016.07.039

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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-sub-bimodules of A and H–H-sub-bisets of G=Gal(L/F), where F=Cent(A), L is the Galois closure of K/F, and H=Gal(L/K). This leads to a combinatorial interpretation of the growth of dimK⁡((KaK)i), for fixed a∈A, especially in terms of Kummer subspaces.",

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AU - Matzri, Eliyahu

AU - Rowen, Louis H.

AU - Saltman, David

AU - Vishne, Uzi

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Y1 - 2017/2/1

N2 - For a maximal separable subfield K of a central simple algebra A, we provide a semiring isomorphism between K–K-sub-bimodules of A and H–H-sub-bisets of G=Gal(L/F), where F=Cent(A), L is the Galois closure of K/F, and H=Gal(L/K). This leads to a combinatorial interpretation of the growth of dimK⁡((KaK)i), for fixed a∈A, especially in terms of Kummer subspaces.

AB - For a maximal separable subfield K of a central simple algebra A, we provide a semiring isomorphism between K–K-sub-bimodules of A and H–H-sub-bisets of G=Gal(L/F), where F=Cent(A), L is the Galois closure of K/F, and H=Gal(L/K). This leads to a combinatorial interpretation of the growth of dimK⁡((KaK)i), for fixed a∈A, especially in terms of Kummer subspaces.

KW - Bimodules

KW - Division algebras

KW - Subfields

UR - https://www.scopus.com/pages/publications/84991573954

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VL - 471

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EP - 479

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Bimodule structure of central simple algebras

Abstract

Bibliographical note

Funding

Keywords

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