Homogeneous SK1 of simple graded algebras

2011/10/30 by Roozbeh Hazrat, R. Hazrat, Adrian R. Wadsworth +3
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.KT #math.RA

paper · pdf · doi:10.48550/arxiv.1110.6585

16 pages

arxiv created 2011/10/30 · openalex publication_date 2011/10/30 · arxiv updated 2011/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a simple graded algebra A=M_n(E) over a graded division algebra E, a short exact sequence relating the reduced Whitehead group of the homogeneous part of A to that of E is established. In particular it is shown that the homogeneous SK1 is not in general Morita invariant.

Citations

• Unitary SK₁ for a Graded Division Ring and its Quotient Division Ring
• Unitary SK₁ of semiramified graded and valued division algebras

Related

• SK1 for graded division algebras
• Unitary SK1 of graded and valued division algebras, I
• Unitary SK₁ of semiramified graded and valued division algebras
• Simple Graded Division Algebras over the Field of Real Numbers
• Finite dimensional graded simple algebras