Dimension quotients of metabelian Lie rings

作者：Passi Inder Bir S^*; Sicking Thomas

来源：International Journal of Algebra and Computation, 2017, 27(2): 251-258.

DOI：10.1142/S0218196717500114

• Lie rings
• Lie dimension subrings
• central series
• universal enveloping algebra

For a Lie ring L over the ring of integers, we compare its lower central series {gamma(n)(L)} n >= 1 and its dimension series {delta(n)(L)} n >= 1 defined by setting dn(L) = L boolean AND pi(n)(L), where pi(L) is the augmentation ideal of the universal enveloping algebra of L. While gamma(n)(L) subset of delta(n)(L) for all n >= 1, the two series can differ. In this paper, it is proved that if L is a metabelian Lie ring, then 2 delta(n)(L) subset of gamma(n)(L), and [delta(n)(L), L] = gamma(n)+1(L), for all n >= 1.

• 出版日期2017-3