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On Characterizing Nilpotent Lie Algebra by Their Multiplier, $$ s(L)=6, 7 $$

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2 Published in 2022 at "Results in Mathematics"

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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0 Published in 2018 at "Frontiers of Mathematics in China"

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

Yamabe Flow On Nilpotent Lie Groups

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1 Published in 2019 at "Bulletin of the Iranian Mathematical Society"

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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0 Published in 2018 at "International Journal of Mathematics"

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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0 Published in 2017 at "Journal of Algebra and Its Applications"

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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1 Published in 2019 at "Quaestiones Mathematicae"

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