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On Weight Systems Derived from Heisenberg Lie Algebras
On Weight Systems Derived from Heisenberg Lie Algebrasopenaire
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Lie superalgebras based on Heisenberg Lie algebras
Linear and Multilinear Algebra, 2020We give a complete classification of real and complex Lie superalgebras based on the Heisenberg Lie algebra h2n+1. This classification generalizes previous classifications.
L. Campa, R. Peniche, G. Salgado
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Generalized Heisenberg Algebras and Toroidal Lie Algebras
Algebra Colloquium, 2010In this article we provide two kinds of infinite presentations of toroidal Lie algebras. At first we define generalized Heisenberg algebras and prove that each toroidal Lie algebra is an amalgamation of a simple Lie algebra and a generalized Heisenberg algebra in the sense of Saito and Yoshii. This is one kind of presentations of toroidal Lie algebras
Fang, Yingjue, Peng, Liangang
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Communications in Algebra, 2011
In this article, we give a sufficient condition for a Lie color algebra to be complete. The color derivation algebra Der(ℋ) and the holomorph L of finite dimensional Heisenberg Lie color algebra ℋ graded by a torsion-free abelian group over an algebraically closed field of characteristic zero are determined.
Hengyun Yang, Naihong Hu
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In this article, we give a sufficient condition for a Lie color algebra to be complete. The color derivation algebra Der(ℋ) and the holomorph L of finite dimensional Heisenberg Lie color algebra ℋ graded by a torsion-free abelian group over an algebraically closed field of characteristic zero are determined.
Hengyun Yang, Naihong Hu
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Solvable Lie algebras with Heisenberg ideals
Journal of Physics A: Mathematical and General, 1993Summary: All finite-dimensional indecomposable solvable Lie algebras \(L(n,f)\), having the Heisenberg algebra \(H(n)\) as the nilradical, are constructed. The number of non-nilpotent elements \(f\) that can be added to \(H(n)\) satisfies \(f\leq n+1\). The Casimir and generalized Casimir operators of the algebras \(L(n,f)\) are obtained.
Rubin, J. L., Winternitz, P.
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q-bosons and the Lie-deformed Heisenberg algebra
Physics Letters A, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pan, Hui-yun, Zhao, Zu Sen
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Complete lie algebras and heisenberg algebras*
Communications in Algebra, 1994(1994). Complete lie algebras and heisenberg algebras. Communications in Algebra: Vol. 22, No. 13, pp. 5509-5524.
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On Weight Systems Derived from Heisenberg Lie Algebras
Journal of Knot Theory and Its Ramifications, 2003Weight systems are constructed with solvable Lie algebras and their infinite dimensional representations. With a Heisenberg Lie algebra and its polynomial representations, the derived weight system vanishes on Jacobi diagrams with positive loop-degree on a circle, and it is proved that the derived knot invariant is the inverse of the Alexander-Conway ...
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Non-Hermitian realization of a Lie-deformed Heisenberg algebra
Physics Letters A, 1995We discuss the non-Hermitian realization of a Lie-deformed, non-canonical Heisenberg algebra. We show that it essentially amounts to the case of a Q-deformed algebra with complex deformation parameter. The (real) energy eigenvalues of the corresponding oscillator are derived, whose deformed spectrum has, among the others, a ground state energy lower ...
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