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Translations in simply transitive affine actions of Heisenberg type Lie groups

Linear Algebra and Its Applications, 2003
Let \((x,y)\mapsto x\cdot y\) be a complete left-symmetric structure on a nilpotent Lie algebra \({\mathfrak g}\). Let \(T({\mathfrak g})\) be the set of \(x\in {\mathfrak g}\) satisfying \(x\cdot y=0\) for all \(y\in {\mathfrak g}\). The left-symmetric structure induces a simply transitive action of a nilpotent Lie group \(G\) such that \(\exp (T ...
Karel Dekimpe, Paul G. Igodt
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Heisenberg subgroups of semisimple Lie groups

Journal of Mathematical Physics, 1975
The restriction of a unitary representation of a semisimple Lie group to a Heisenberg subgroup Hn is shown to be quasiequivalent to the regular representation of Hn. Spectral properties of elements of the Heisenberg subgroup are described. Conditions under which an element of a semisimple Lie algebra may be embedded in a Heisenberg algebra are found.
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Heisenberg–Pauli–Weyl inequality for connected nilpotent Lie groups

International Journal of Mathematics, 2018
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 important role in the proof.
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Properties of harmonic measures in the Dirichlet problem for nilpotent Lie groups of Heisenberg type

American Journal of Mathematics, 2002
In groups of Heisenberg type we introduce a large class of domains, which we call ADP, admissible for the Dirichlet problem , and we prove that on the boundary of such domains, harmonic measure, ordinary surface measure, and the perimeter measure, are mutually absolutely continuous.
CAPOGNA L., GAROFALO, NICOLA, NHIEU D. M.   +2 more
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Optimal control analysis and PID controller design for the Heisenberg Lie group H(3)

2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), 2016
This work is a study on left-invariant, drift free optimal control problem on H(3) Lie group. The control objective is to minimize the cost function and steer the system in non-ideal environment. The stability of the resulting dynamics has been studied and PID controllers have been designed at the equilibrium points.
Soumya Ranjan Sahoo, Amit Jena
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Integration by parts and Bismut-Elworthy-Li-type formula on the Heisenberg Lie group using the hypoelliptic measure

Physica Scripta
Abstract We study left-invariant vector fields defined on the Heisenberg Lie group and the associated stochastic differential equation, expressed in terms of a hypoelliptic operator. Utilizing the Bismut tangent space, we derive a new integration by parts formula on the path space of the Heisenberg Lie group using the hypoelliptic ...
Roberta R Albuquerque, Antônio M S Macêdo, Raydonal Ospina   +2 more
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Analog radar signal design and digital signal processing —a Heisenberg nilpotent Lie group approach

2008
The notions of analog and digital radar auto- and cross-ambiguity functions are on the borderline with mathematics, physics, and electrical engineering. This paper presents the solutions of two problems of analog radar signal design: the synthesis problem (posed in 1953) and the invariance problem for ambiguity surfaces over the symplectic time ...
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Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra

Mathematics, 2023
Xue Chen
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Representations of super deformation of Heisenberg-Virasoro type Lie conformal algebras

Communications in Algebra, 2023
Chunguang Xia
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Lie superalgebras based on Heisenberg Lie algebras

Linear and Multilinear Algebra, 2020
Gil Salgado
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