Malcev Lie algebra
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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 together with a complete, descending -vector space filtration , such that:
- the associated graded Lie algebra is generated by elements of degree one.
Malcev Lie algebras come up, e.g., in the theory of mixed Hodge structures.
References
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