2011/07/15 by Roozbeh Hazrat, R. Hazrat, Z. Zhang +3
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1107.3056
arxiv created 2011/07/15 · openalex publication_date 2011/07/15 · arxiv updated 2011/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let Ii, i=0,...,m, be two-sided ideals of A, \GLn(A,Ii) the principal congruence subgroup of level Ii in GLn(A) and En(A,Ii) be the relative elementary subgroup of level Ii. We prove a multiple commutator formula [En(A,I0),\GLn(A,I1),& \GLn(A, I2),..., \GLn(A, Im)] = [En(A,I0),En(A,I1),En(A, I2),..., En(A, Im)], which is a broad generalization of the standard commutator formulas.