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Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra
Mathematics, 2023 The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations.
Xue Chen
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On Properties of the (2n+1)-Dimensional Heisenberg Lie Algebra
JTAM (Jurnal Teori dan Aplikasi Matematika), 2020 In the present paper, we study some properties of the Heisenberg Lie algebra of dimension . The main purpose of this research is to construct a real Frobenius Lie algebra from the Heisenberg Lie algebra of dimension .
Edi Kurniadi
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Deformations of the Heisenberg Lie algebra
Journal of Physics: Conference Series, 2021 Abstract In this note we compute all deformations of the 3-dimensional Heisenberg Lie algebra ℌ3. This shows that ℌ3 deforms to almost all Lie algebras of dimension 3.
Maria Alejandra Alvarez
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Quantum metrology with linear Lie algebra parameterizations [PDF]
Physical Review Research, 2023 Lie algebraic techniques are powerful and widely used tools for studying dynamics and metrology in quantum optics. When the Hamiltonian generates a Lie algebra with finite dimension, the unitary evolution can be expressed as a finite product of ...
Ruvi Lecamwasam +2 more
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On the cohomology of extensions by a Heisenberg Lie algebra [PDF]
Bulletin of the Australian Mathematical Society, 2005 This article describes the cohomology spaces of any Lie algebra containing a Lie algebra of Heisenberg type (whose cohomology was studied by Santharoubane) as an ideal of codimension 1. For instance, the twisted standard filiform Lie algebras are of this kind.
H. Pouseele
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Yang-Baxter deformations of WZW model on the Heisenberg Lie group [PDF]
Nuclear Physics B, 2021 The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group (H4) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the h4 Lie algebra by using its
Ali Eghbali +2 more
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A representation of Weyl–Heisenberg Lie algebra in the quaternionic setting [PDF]
Annals of Physics, 2017 Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the so-obtained position and momentum operators, we study the Heisenberg uncertainty principle on the whole set of ...
Muraleetharan, B. +2 more
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On the cohomology of restricted Heisenberg Lie algebras [PDF]
Linear Algebra and its ApplicationsWe show that the Heisenberg Lie algebras over a field $\mathbb{F}$ of characteristic $p>0$ admit a family of restricted Lie algebras, and we classify all such non-isomorphic restricted Lie algebra structures. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 1- and 2-cohomology spaces of these ...
Evans, Tyler J. +2 more
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Bosonic Realizations of the Colour Heisenberg Lie Algebra [PDF]
Journal of Nonlinear Mathematical Physics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sigurdsson, Gunnar +1 more
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On the Property M Conjecture for the Heisenberg Lie Algebra
Journal of Combinatorial Theory, Series A, 2002 Let \({\mathcal H}_3\) be the three dimensional complex Heisenberg Lie algebra consisting of strictly upper triangular \(3\times 3\) matrices over \(\mathbb{C}\). Let \(e = z_{12}\), \(f= z_{23}\), \(x= z_{13}\) be the standard basis of \({\mathcal H}_3\), where \(z_{ij}\) is the matrix with 1 as the \((i,j)\)th entry and 0's elsewhere.
Phil Hanlon, Michelle L. Wachs
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