On Characterizing Nilpotent Lie Algebra by Their Multiplier, $$ s(L)=6, 7 $$
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DOI: 10.1007/s00025-022-01616-5
Abstract: Let L be an n-dimensional non-abelian nilpotent Lie algebra and s(L) = 1 2 (n − 1)(n − 2) + 1 − dimM(L) where M(L) is the Schur multiplier of a Lie algebra L. The… read more here.
Keywords: lie; lie algebra; nilpotent lie; algebra multiplier ... See more keywords
Non-embedding theorems of nilpotent Lie groups and sub-Riemannian manifolds
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DOI: 10.1007/s11464-020-0823-3
Abstract: We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension condition RCD (0, N ) with… read more here.
Keywords: nilpotent lie; non embedding; lie groups; embedding theorems ... See more keywords
Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds
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DOI: 10.1007/s13324-025-01051-z
Abstract: In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these… read more here.
Keywords: nilpotent lie; lie groups; calculus; semiclassical functional ... See more keywords
Yamabe Flow On Nilpotent Lie Groups
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DOI: 10.1007/s41980-019-00317-0
Abstract: In this paper, we consider the Yamabe flow on Lie groups with left invariant metrics in particular case on the higher dimensional classical Heisenberg nilpotent Lie groups and the higher dimensional quaternion Lie groups. We… read more here.
Keywords: groups yamabe; lie; nilpotent lie; lie groups ... See more keywords
Heisenberg–Pauli–Weyl inequality for connected nilpotent Lie groups
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DOI: 10.1142/s0129167x18500866
Abstract: The purpose of this paper is to formulate and prove an analogue of the classical Heisenberg–Pauli–Weyl uncertainty inequality for connected nilpotent Lie groups with noncompact center. Representation theory and a localized Plancherel formula play an… read more here.
Keywords: heisenberg pauli; pauli weyl; nilpotent lie; connected nilpotent ... See more keywords
Central automorphisms of free nilpotent Lie algebras
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DOI: 10.1142/s021949881750205x
Abstract: Let ℒm,n be the free nilpotent Lie algebra of finite rank m, m ≥ 2 and nilpotency class n − 1 over a field of characteristic zero. We give a characterization of central automorphisms of… read more here.
Keywords: lie algebras; nilpotent lie; free nilpotent; automorphisms free ... See more keywords
Nilpotent lie algebras having the Schur multiplier of maximum dimension
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DOI: 10.2989/16073606.2019.1606123
Abstract: Abstract Let L be an n-dimensional nilpotent Lie algebra of nilpotency class c with the derived subalgebra of dimension m. Recently, Rai proved that the dimension of Schur multiplier of L is bounded by .… read more here.
Keywords: dimension; schur multiplier; lie; lie algebras ... See more keywords
Homomorphic Cryptographic Scheme Based on Nilpotent Lie Algebras for Post-Quantum Security
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DOI: 10.3390/sym17101666
Abstract: In this paper, the use of nilpotent Lie algebras as the basis for homomorphic encryption based on additive operations is explored. The g-setting is set up over gln(Zq)) and the group G=exp(g), and it is… read more here.
Keywords: scheme; nilpotent lie; security; homomorphic cryptographic ... See more keywords