Multiple Commutator Formulas
Abstract
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, n(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),n(A,I1),& n(A, I2),..., n(A, Im)] = [En(A,I0),En(A,I1),En(A, I2),..., En(A, Im)], which is a broad generalization of the standard commutator formulas.
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