MULTIPLE COMMUTATOR FORMULAS

作者：Hazrat, Roozbeh^*; Zhang, Zuhong

来源：Israel Journal of Mathematics, 2013, 195(1): 481-505.

DOI：10.1007/s11856-012-0135-8

• SUBGROUPS
• GL(N,A)

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) be 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 the 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. This result contains all the published results on commutator formulas over commutative rings and answers a problem posed by A. Stepanov and N. Vavilov.

• 出版日期2013-6
• 单位北京理工大学