An azumaya algebra version of the kneser-tits problem for groups of type D4

L. H. Rowen; D. Saltman; Y. Segev; U. Vishne

doi:10.1080/00927870903447221

An azumaya algebra version of the kneser-tits problem for groups of type D₄

L. H. Rowen, D. Saltman, Y. Segev, U. Vishne

Department of Mathematics

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

Abstract

We solve the following problem related to the Kneser-Tits conjecture, for Azumaya algebras. Given an Azumaya algebra D of rank 4 that is not a division algebra, whose center K is three-dimensional over the ground field F, such that cor_K/FD is trivial, is it true that every element of D having reduced norm in F is a product of n elements having both reduced norm and reduced trace in F? This is true for n ≥ 3, but false for n = 2.

Original language	English
Pages (from-to)	133-152
Number of pages	20
Journal	Communications in Algebra
Volume	39
Issue number	1
DOIs	https://doi.org/10.1080/00927870903447221
State	Published - 2010

Bibliographical note

Funding Information:
This research was partially supported by BSF grant no. 2004-083.

Funding

This research was partially supported by BSF grant no. 2004-083.

Funders	Funder number
United States-Israel Binational Science Foundation	2004-083

Keywords

Azumaya algebra
Division algebra
Kneser-Tits problem
Quaternions
Whitehead group

Access to Document

10.1080/00927870903447221

Cite this

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abstract = "We solve the following problem related to the Kneser-Tits conjecture, for Azumaya algebras. Given an Azumaya algebra D of rank 4 that is not a division algebra, whose center K is three-dimensional over the ground field F, such that corK/FD is trivial, is it true that every element of D having reduced norm in F is a product of n elements having both reduced norm and reduced trace in F? This is true for n ≥ 3, but false for n = 2.",

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