Multiple Commutator Formulas
Rings and Algebras
2011-07-18 v1
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.
Keywords
Cite
@article{arxiv.1107.3056,
title = {Multiple Commutator Formulas},
author = {R. Hazrat and Z. Zhang},
journal= {arXiv preprint arXiv:1107.3056},
year = {2011}
}