scholarly journals Harmonic analysis on the quotient spaces of Heisenberg groups

1991 ◽  
Vol 123 ◽  
pp. 103-117 ◽  
Author(s):  
Jae-Hyun Yang
Keyword(s):  
Quantum Mechanics ◽  
Heisenberg Group ◽  
Harmonic Analysis ◽  
Unitary Representation ◽  
Lie Group ◽  
Theta Series ◽  
Foundations Of Quantum Mechanics ◽  
Nilpotent Lie Group ◽  
Heisenberg Groups ◽  
Quotient Spaces

A certain nilpotent Lie group plays an important role in the study of the foundations of quantum mechanics ([Wey]) and of the theory of theta series (see [C], [I] and [Wei]). This work shows how theta series are applied to decompose the natural unitary representation of a Heisenberg group.

scholarly journals Generalized Ricci flow on nilpotent Lie groups

2021 ◽  
Vol 33 (4) ◽  
pp. 997-1014
Author(s):  
Fabio Paradiso
Keyword(s):  
Heisenberg Group ◽  
Lie Group ◽  
Ricci Flow ◽  
Nilpotent Lie Groups ◽  
Nilpotent Lie Group ◽  
Geometric Flows ◽  
Courant Algebroid ◽  
New Family ◽  
Lie Brackets ◽  
Simply Connected

Abstract We define solitons for the generalized Ricci flow on an exact Courant algebroid. We then define a family of flows for left-invariant Dorfman brackets on an exact Courant algebroid over a simply connected nilpotent Lie group, generalizing the bracket flows for nilpotent Lie brackets in a way that might make this new family of flows useful for the study of generalized geometric flows such as the generalized Ricci flow. We provide explicit examples of both constructions on the Heisenberg group. We also discuss solutions to the generalized Ricci flow on the Heisenberg group.

scholarly journals Representasi Unitar Tak Tereduksi Grup Lie Dari Aljabar Lie Filiform Real Berdimensi 5

2020 ◽  
Vol 17 (1) ◽  
pp. 100-108
Author(s):  
E Kurniadi
Keyword(s):  
Harmonic Analysis ◽  
Lie Algebra ◽  
Unitary Representation ◽  
Lie Group ◽  
Dual Space ◽  
Irreducible Unitary Representation ◽  
Coadjoint Orbits ◽  
Dimensional Representation ◽  
Induced Representation ◽  
Filiform Lie Algebra

In this paper, we study a harmonic analysis of a Lie group  of a real filiform Lie algebra of dimension 5. Particularly, we study its  irreducible unitary representation (IUR) and contruct this IUR corresponds to its coadjoint orbits through coadjoint actions of its group to its dual space.  Using induced representation of  a 1-dimensional representation of its subgroup we obtain its IUR of its Lie group

scholarly journals On the isomorphism problem for C∗-algebras of nilpotent Lie groups

2019 ◽  
pp. 1-30
Author(s):  
Ingrid Beltiţă ◽  
Daniel Beltiţă
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Isomorphism Problem ◽  
Nilpotent Lie Groups ◽  
Direct Products ◽  
Nilpotent Lie Group ◽  
Heisenberg Groups ◽  
C Algebras ◽  
Dimension Formula ◽  
Unitary Dual

We investigate to what extent a nilpotent Lie group is determined by its [Formula: see text]-algebra. We prove that, within the class of exponential Lie groups, direct products of Heisenberg groups with abelian Lie groups are uniquely determined even by their unitary dual, while nilpotent Lie groups of dimension [Formula: see text] are uniquely determined by the Morita equivalence class of their [Formula: see text]-algebras. We also find that this last property is shared by the filiform Lie groups and by the [Formula: see text]-dimensional free two-step nilpotent Lie group.

scholarly journals Parameter rigid actions of simply connected nilpotent Lie groups

2012 ◽  
Vol 33 (6) ◽  
pp. 1864-1875 ◽  
Author(s):  
HIROKAZU MARUHASHI
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Compact Manifold ◽  
Nilpotent Lie Groups ◽  
Nilpotent Lie Group ◽  
Heisenberg Groups ◽  
Dense Orbit ◽  
Simply Connected

AbstractWe show that for a locally free $C^{\infty }$-action of a connected and simply connected nilpotent Lie group on a compact manifold, if every real-valued cocycle is cohomologous to a constant cocycle, then the action is parameter rigid. The converse is true if the action has a dense orbit. Using this, we construct parameter rigid actions of simply connected nilpotent Lie groups whose Lie algebras admit rational structures with graduations. This generalizes the results of dos Santos [Parameter rigid actions of the Heisenberg groups. Ergod. Th. & Dynam. Sys.27(2007), 1719–1735] concerning the Heisenberg groups.

scholarly journals Some results on harmonic analysis on compact quotients of heisenberg groups

1985 ◽  
Vol 99 ◽  
pp. 45-62 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Heisenberg Group ◽  
Nilpotent Group ◽  
Harmonic Analysis ◽  
Matrix Group ◽  
Heisenberg Groups ◽  
Dimension 2 ◽  
The Law

Heisenberg group H2g+1(R) of dimension 2g + 1 is a real nilpotent group defined on R × Rg × Rg by the law of composition which is isomorphic to the unipotent matrix group

scholarly journals On seven-dimensional quaternionic contact solvable Lie groups

2014 ◽  
Vol 26 (2) ◽  
Author(s):  
Diego Conti ◽  
Marisa Fernández ◽  
José A. Santisteban
Keyword(s):  
Heisenberg Group ◽  
Lie Groups ◽  
Lie Group ◽  
Contact Structure ◽  
Contact Manifold ◽  
Nilpotent Lie Group ◽  
Solvable Lie Groups ◽  
Quaternionic Heisenberg Group

AbstractWe answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven-dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach to the classification of seven-dimensional solvable Lie groups having an integrable left invariant quaternionic contact structure. In particular, we prove that the unique seven-dimensional nilpotent Lie group admitting such a structure is the quaternionic Heisenberg group.

scholarly journals Transitivity of Heisenberg group extensions of hyperbolic systems

2011 ◽  
Vol 32 (1) ◽  
pp. 223-235 ◽  
Author(s):  
IAN MELBOURNE ◽  
VIOREL NIŢICĂ ◽  
ANDREI TÖRÖK
Keyword(s):  
Dynamical System ◽  
Heisenberg Group ◽  
Lie Group ◽  
Commutator Subgroup ◽  
Hyperbolic Systems ◽  
Nilpotent Lie Group ◽  
Topological Transitivity ◽  
Group Extensions ◽  
Topologically Transitive ◽  
Dimension 2

AbstractWe show that amongCrextensions (r>0) of a uniformly hyperbolic dynamical system with fiber the standard real Heisenberg group ℋnof dimension 2n+1, those that avoid an obvious obstruction to topological transitivity are generically topologically transitive. Moreover, if one considers extensions with fiber a connected nilpotent Lie group with a compact commutator subgroup (for example ℋn/ℤ), among those that avoid the obvious obstruction, topological transitivity is open and dense.

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