2009/11/18 by Roozbeh Hazrat, R. Hazrat, Adrian R. Wadsworth +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras #math.KT
paper · pdf · doi:10.48550/arxiv.0911.3628
arxiv created 2009/11/18 · openalex publication_date 2009/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The reduced unitary Whitehead group SK1 of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary SK1 of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary SK1 of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary SK1 for much wider classes of division algebras over henselian fields.