2026/06/02 by Vijay R. Tiwari, Selby Jose
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Geometric and Algebraic Topology #Group (periodic table) #Order (exchange) #Structured program theorem #Unimodular matrix #Vector space
paper · doi:10.1080/03081087.2026.2681150
openalex publication_date 2026/06/02 · openalex created_date 2026/06/04 · openalex updated_date 2026/07/26
In this article, we study special 2×n row Suslin matrices Sn2(V,W), arising from the pair of matrices V,W∈M2,n(R) with V.WT=I2. These matrices generate a subgroup SUmn2(R) of the general linear group GL22n−1(R). Our primary focus is on the elementary subgroup EUmn2(R)⊂SL22n−1(R) of SUmn2(R), for which we determine a complete set of generators by establishing the key lemma. We further investigate the algebraic properties of these generators and prove a structure theorem for EUmn2(R) that simplifies the generating set. The findings presented in this article enhance the understanding of matrix group generation and have potential implications for algebraic K-theory and related areas.