Nilpotent lie group - Open Access .click

Journal of Lie Theory, 2020
Summary: For a closed subsemigroup \(S\) of a simply connected nilpotent Lie group \(G\), we prove that either \(S\) is a subgroup, or there is an epimorphism \(f\) from \(G\) to the reals \(R\) such that \(f(s) \ge 0\) for all \(s\) of \(S\).
Abels, Herbert, Vinberg, Ernest B.
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Uncertainty relations on nilpotent Lie groups [PDF]

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017
We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups.
Michael Ruzhansky, Durvudkhan Suragan
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Lie-Nilpotency Indices of Group Algebras

Bulletin of the London Mathematical Society, 1992
For an associative ring \(A\), define \(A^{[1]}\) to be \(A\) and \(A^{[n]}\) (\(n>1\)) to be the two-sided ideal of \(A\) that is generated by all \(n\)- fold Lie commutators \([a_ 1,[a_ 2,\dots,[a_{n-1},a_ n]\dots]]\) (\(a_ i\in A\)). \(A\) is called Lie-nilpotent if \(A^{[n]}=0\) for some \(n\), in which case the smallest such \(n\) is denoted \(t_ ...
Bhandari, Ashwani K., Passi, I. B. S.
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mathematics
carnot groups
53c17

nilpotent lie groups
43a80
radioactivity

22e25
atomic energy
nuclear and particle physics