Results 61 to 70 of about 312 (162)

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.
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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.
Hanlon, Phil, Wachs, Michelle L.
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Irreducible modules for map Heisenberg–Virasoro Lie algebras

Journal of Algebra and Its Applications
We study irreducible modules for map Heisenberg–Virasoro algebras. In particular, we give a complete classification of irreducible Harish–Chandra modules for map Heisenberg–Virasoro algebras. We will also classify non-weight irreducible modules for map Heisenberg–Virasoro algebras whose restriction on the degree zero part of the universal enveloping ...
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Lie Bialgebra Structures on Generalized Heisenberg-Virasoro Algebra

, 2012
In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie bialgebra structure on centerless generalized Heisenberg-Virasoro algebra $\bar{\mathfrak{L}}$ are coboundary ...
Chen, Haibo, Shen, Ran, Zhang, Jiangang
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Restricted Cohomology of Heisenberg Lie Algebras

arXiv admin note: text overlap with arXiv:2402.14249.
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Deformations of the five dimensional Heisenberg Lie algebra

Journal of Mathematical Physics
In this note we explicitly give all the equivalent classes of deformations of the five-dimensional Heisenberg Lie algebra h2 over C or R. We show that there are altogether 20 infinitesimal deformations (families), 18 of them being extendable to real deformations and 2 of them are only infinitesimal.
Alice Fialowski, Ashis Mandal
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Lie structure of the Heisenberg-Weyl algebra

International Electronic Journal of Algebra
As an associative algebra, the Heisenberg--Weyl algebra $\HWeyl$ is generated by two elements $A$, $B$ subject to the relation $AB-BA=1$. As a Lie algebra, however, where the usual commutator serves as Lie bracket, the elements $A$ and $B$ are not able to generate the whole space $\HWeyl$.
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Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras

, 2011
23 pages; to appear in Frontiers of Mathematics in ...
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Horizontally Affine Functions on Step-2 Carnot Algebras. [PDF]

J Geom Anal, 2023
Le Donne E, Morbidelli D, Rigot S.
europepmc   +1 more source

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups. [PDF]

Entropy (Basel), 2023
Jackson CS, Caves CM.
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