Results 21 to 30 of about 68,205 (182)

Computing the index of Lie algebras; pp. 265–271 [PDF]

Proceedings of the Estonian Academy of Sciences, 2010
The aim of this paper is to compute and discuss the index of Lie algebras. We consider the n-dimensional Lie algebras for n lt; 5 and the case of filiform Lie algebras which form a special class of nilpotent Lie algebras.
Hadjer Adimi, Abdenacer Makhlouf
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The classification of three-dimensional Lie algebras on complex field

Дифференциальная геометрия многообразий фигур, 2021
In this paper, we study the classification of three-dimensional Lie al­gebras over a field of complex numbers up to isomorphism. The proposed classification is based on the consideration of objects invariant with re­spect to isomorphism, namely such ...
E.R. Shamardina
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HEISENBERG-LIE COMMUTATION RELATIONS IN BANACH ALGEBRAS [PDF]

Mathematical Proceedings of the Royal Irish Academy, 2009
Let \(q_1\) and \(q_2\) be nonzero complex numbers. We say that three elements \(b_1, b_2\) and \(b_3\) of a complex algebra satisfy the \((q_1, q_2)\)-deformed Heisenberg-Lie commutation relations if \(b_1b_2-q_1b_2b_1=b_3\), \(q_2b_1b_3-b_3b_1=0\) and \(b_2b_3-q_2b_3b_2=0\). In the paper under review, the authors construct a unital Banach algebra \({\
Laustsen, Niels Jakob, Silvestrov, Sergei D.   +1 more
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Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems

Universe, 2022
This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and ...
Anatolij K. Prykarpatski
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Restricted modules and associated vertex algebras of extended Heisenberg-Virasoro algebra [PDF]

Journal of Algebra, 2023
In this paper, a family of infinite dimensional Lie algebras $\tilde{\mathcal{L}}$ is introduced and investigated, called the extended Heisenberg-Virasoro algebra,denoted by $\tilde{\mathcal{L}}$.
Hongyan Guo, Huaimin Li
semanticscholar   +1 more source

An Introduction to Noncommutative Physics

Physics, 2023
Noncommutativity in physics has a long history, tracing back to classical mechanics. In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras.
Shi-Dong Liang, Matthew J. Lake
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The linear $\protect \mathfrak{n}(1|N)$–invariant differential operators and $\protect \mathfrak{n}(1|N)$–relative cohomology

Comptes Rendus. Mathématique, 2020
Over the $(1,N)$-dimensional supercircle $S^{1|N}$, we classify $\mathfrak{n}(1|N)$-invariant linear differential operators acting on the superspaces of weighted densities on $S^{1|N}$, where $\mathfrak{n}(1|N)$ is the Heisenberg Lie superalgebra.
Khalfoun, Hafedh, Laraiedh, Ismail
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Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework [PDF]

Journal of Physics A: Mathematical and Theoretical
We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups Z32, Z2p×Z32 for p=1,2,3, and investigate the properties of their associated multi-particle quantum paraoscillators.
Z. Kuznetsova, F. Toppan
semanticscholar   +1 more source

Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit–qubit interaction

Scientific Reports, 2021
The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit–qubit interaction and dissipation term is considered.
S. Abdel-Khalek, Hashim M. Alshehri, E. M. Khalil, A.-S. F. Obada   +3 more
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On the centroid of Heisenberg Lie algebra

四川大学学报. 自然科学版, 2023
Heisenberg Lie algebra belongs to a class of solvable Lie algebra. It has a deep physical background and thus is an important object of Lie algebra study.
YU De-Ming, MA Jie-Jing, JIANG Chan
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