Bimodule structure of central simple algebras

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

doi:https://doi.org/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

Bar-Ilan University

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

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

Keywords

Bimodules
Division algebras
Subfields

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

https://doi.org/10.1016/j.jalgebra.2016.07.039

Cite this

@article{d9b5e9f10bee46a9af56fb82c55299f4,

title = "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-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.",

keywords = "Bimodules, Division algebras, Subfields",

author = "Eliyahu Matzri and Rowen, {Louis H.} and David Saltman and Uzi Vishne",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

month = feb,

day = "1",

doi = "https://doi.org/10.1016/j.jalgebra.2016.07.039",

language = "الإنجليزيّة",

volume = "471",

pages = "454--479",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Bimodule structure of central simple algebras

AU - Matzri, Eliyahu

AU - Rowen, Louis H.

AU - Saltman, David

AU - Vishne, Uzi

PY - 2017/2/1

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 - http://www.scopus.com/inward/record.url?scp=84991573954&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.jalgebra.2016.07.039

DO - https://doi.org/10.1016/j.jalgebra.2016.07.039

M3 - مقالة

SN - 0021-8693

VL - 471

SP - 454

EP - 479

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Bimodule structure of central simple algebras

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this