Unitary SK₁ of semiramified graded and valued division algebras

2010/09/20 by Adrian R. Wadsworth, A. R. Wadsworth, Wadsworth, A. R. · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.KT #math.RA

paper · pdf · doi:10.48550/arxiv.1009.3904

34 pages. Correction in References in v. 2

openalex publication_date 2010/09/20 · arxiv created 2010/09/22 · arxiv updated 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove formulas for the unitary SK₁ of a semiramified graded division algebra (or valued division algebra over a Henselian field) with a unitary involution. These formulas generalize earlier formulas of Yanchevskii, (and Platonov and Ershov for the nonunitary SK₁).

Cited by

• Unitary SK₁ for a Graded Division Ring and its Quotient Division Ring
• Homogeneous SK1 of simple graded algebras

Related

• Unitary SK1 of graded and valued division algebras, I
• Unitary SK₁ for a Graded Division Ring and its Quotient Division Ring
• Homogeneous SK1 of simple graded algebras
• SK1 for graded division algebras
• Galois extensions, positive involutions and an application to unitary space-time coding