Solvability of the \rm SK₁-analog of the orthogonal groups

2025/04/23 by A. A. Ambily, A., Ambily A., Gayathry Pradeep +1
Mathematics · #11E70 #13C10 #13H99 #19G99 #20F16 #20H25 #Algebraic and Geometric Analysis #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2504.16509

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We prove the dilation principle for the relative Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group and using the dilation principle we prove the Quillen's analog of the local-global principle for the group. Applying the relative local-global principle, we prove the solvability and nilpotency of the \rm SK₁-analog of the orthogonal groups and study the homotopy and commutativity principle for odd elementary orthogonal groups.

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