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arXiv · 1107.3056

Multiple Commutator Formulas

R. Hazrat·Z. Zhang
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Abstract

Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I_i, i=0,...,m, be two-sided ideals of A, \GL_n(A,I_i) the principal congruence subgroup of level I_i in GL_n(A) and E_n(A,I_i) be the relative elementary subgroup of level I_i. We prove a multiple commutator formula [E_n(A,I_0),\GL_n(A,I_1),& \GL_n(A, I_2),..., \GL_n(A, I_m)] = [E_n(A,I_0),E_n(A,I_1),E_n(A, I_2),..., E_n(A, I_m)], which is a broad generalization of the standard commutator formulas.

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R. Hazrat, Z. Zhang. 2011-07-15. Multiple Commutator Formulas. https://arxiv.org/abs/1107.3056

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