Square-central elements and standard generators for biquaternion algebras

Adam Chapman; Uzi Vishne

doi:10.1007/s11856-013-0005-z

Square-central elements and standard generators for biquaternion algebras

Adam Chapman
, Uzi Vishne

Department of Mathematics

Bar-Ilan University

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

3 Scopus citations

Abstract

Analyzing square-central elements in central simple algebras of degree 4, we show that every two elementary abelian Galois maximal subfields are connected by a chain of nontrivially-intersecting pairs. Similar results are proved for non-central quaternion subalgebras, and for central quaternion subalgebras when they exist. Along these lines we classify the maximal square-central subspaces. We also show that every two standard quadruples of generators of a biquaternion algebra are connected by a chain of basic steps, in each of which at most two generators are being changed.

Original language	English
Pages (from-to)	409-423
Number of pages	15
Journal	Israel Journal of Mathematics
Volume	197
Issue number	1
DOIs	https://doi.org/10.1007/s11856-013-0005-z
State	Published - Oct 2013

Bibliographical note

Funding Information:
∗ This work was supported by the U.S.-Israel Binational Science Foundation (grant no. 2010/149). Received January 19, 2012 and in revised form June 13, 2012

Funding

∗ This work was supported by the U.S.-Israel Binational Science Foundation (grant no. 2010/149). Received January 19, 2012 and in revised form June 13, 2012

Funders	Funder number
United States-Israel Binational Science Foundation	2010/149

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10.1007/s11856-013-0005-z

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abstract = "Analyzing square-central elements in central simple algebras of degree 4, we show that every two elementary abelian Galois maximal subfields are connected by a chain of nontrivially-intersecting pairs. Similar results are proved for non-central quaternion subalgebras, and for central quaternion subalgebras when they exist. Along these lines we classify the maximal square-central subspaces. We also show that every two standard quadruples of generators of a biquaternion algebra are connected by a chain of basic steps, in each of which at most two generators are being changed.",

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Square-central elements and standard generators for biquaternion algebras

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