Stability of unitary SK1 of Azumaya algebras

Roozbeh Hazrat

doi:10.1007/s00013-011-0338-y

Stability of unitary SK1 of Azumaya algebras

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Abstract

For an Azumaya algebra A with center C of rank n 2 and a unitary involution τ, we study the stability of the unitary SK1 under reduction. We show that if R = C τ is a Henselian ring with maximal ideal m and 2 and n are invertible in R then SK1(A,τ) ≅ SK1(A/mA, overlineτ).

Original language	English
Pages (from-to)	19-23
Number of pages	5
Journal	Archiv der Mathematik
Volume	98
Issue number	1
DOIs	https://doi.org/10.1007/s00013-011-0338-y
Publication status	Published - 2012

Keywords

Azumaya algebras
reduced Whitehead group
unitary involution

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10.1007/s00013-011-0338-y

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title = "Stability of unitary SK1 of Azumaya algebras",

abstract = "For an Azumaya algebra A with center C of rank n 2 and a unitary involution τ, we study the stability of the unitary SK1 under reduction. We show that if R = C τ is a Henselian ring with maximal ideal m and 2 and n are invertible in R then SK1(A,τ) ≅ SK1(A/mA, overlineτ).",

keywords = "Azumaya algebras, reduced Whitehead group, unitary involution",

author = "Roozbeh Hazrat",

year = "2012",

doi = "10.1007/s00013-011-0338-y",

language = "English",

volume = "98",

pages = "19--23",

journal = "Archiv der Mathematik",

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TY - JOUR

T1 - Stability of unitary SK1 of Azumaya algebras

AU - Hazrat, Roozbeh

PY - 2012

Y1 - 2012

N2 - For an Azumaya algebra A with center C of rank n 2 and a unitary involution τ, we study the stability of the unitary SK1 under reduction. We show that if R = C τ is a Henselian ring with maximal ideal m and 2 and n are invertible in R then SK1(A,τ) ≅ SK1(A/mA, overlineτ).

AB - For an Azumaya algebra A with center C of rank n 2 and a unitary involution τ, we study the stability of the unitary SK1 under reduction. We show that if R = C τ is a Henselian ring with maximal ideal m and 2 and n are invertible in R then SK1(A,τ) ≅ SK1(A/mA, overlineτ).

KW - Azumaya algebras

KW - reduced Whitehead group

KW - unitary involution

UR - http://handle.uws.edu.au:8081/1959.7/516529

U2 - 10.1007/s00013-011-0338-y

DO - 10.1007/s00013-011-0338-y

M3 - Article

SN - 1420-8938

SN - 0003-889X

VL - 98

SP - 19

EP - 23

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 1

ER -

Stability of unitary SK1 of Azumaya algebras

Abstract

Keywords

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