Malcev Lie algebra

In mathematics, a Malcev Lie algebra, or Mal'tsev Lie algebra, is a generalization of a rational nilpotent Lie algebra, and Malcev groups are similar. Both were introduced by Quillen (1969, Appendix A3), based on the work of (Mal'cev 1949).

According to Papadima & Suciu (2004) a Malcev Lie algebra is a rational Lie algebra L together with a complete, descending Q -vector space filtration { F r L } r ≥ 1 , such that:

Malcev Lie algebras come up, e.g., in the theory of mixed Hodge structures.