Results 141 to 150 of about 68,205 (182)

On Extensions of Lie Algebras by Means of the Heisenberg Algebra

Mathematical Notes, 2005
We prove that extensions of an arbitrary algebra generated by the Heisenberg algebra are inessential after factorization with respect to the center of the Heisenberg algebra. The extensions considered in the paper have a standard description in terms of a pair consisting of a representation and a cohomology class.
exaly   +2 more sources

A very proper Heisenberg–Lie Banach *-algebra

Positivity, 2011
For each pair of non-zero real numbers q1 and q2, Laustsen and Silvestrov have constructed a unital Banach *-algebra \({\fancyscript{C}_{q_1,q_2}}\) which contains a universal normalized solution to the *-algebraic (q1, q2)-deformed Heisenberg–Lie commutation relations. We show that for (q1, q2) = (−1, 1), this Banach *-algebra is very proper; that is,
Niels Jakob Laustsen
exaly   +2 more sources

Transposed Poisson structures on loop Heisenberg-Virasoro Lie algebra

Bulletin of the Belgian Mathematical Society - Simon Stevin
Yang Yang, Xiaomin Tang
exaly   +2 more sources

Local and Linear 2-local Automorphisms of Heisenberg Lie (Super)algebras

Frontiers of Mathematics
Wende Liu, Liu Wende
exaly   +2 more sources

Generalized Heisenberg Algebras and Toroidal Lie Algebras

Algebra Colloquium, 2010
In 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
openaire   +2 more sources

Characterizations of Heisenberg-like Lie Algebras

Journal of Lie Theory, 2011
The authors give a characterizations of Heisenberg-like Lie algebras. They also present infinite families of examples of Heisenberg-like Lie algebras which are not Heisenberg-like.
DeCoste, Rachelle C., DeMeyer, Lisa, Mast, Maura B.   +2 more
openaire   +2 more sources

Minimal Faithful Representation of the Heisenberg Lie Algebra with Abelian Factor

Journal of Lie theory, 2012
For a finite dimensional Lie algebra $\g$ over a field $\k$ of characteristic zero, the $\mu$-function (respectively $\mu_{nil}$-function) is defined to be the minimal dimension of $V$ such that $\g$ admits a faithful representation (respectively a ...
N. Rojas
semanticscholar   +1 more source

Heisenberg Lie Color Algebras

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
openaire   +1 more source

Lie algebra and Dynkin index

Communications in Algebra, 2023
The Lie algebra comes from P. Deligne’s work on the exceptional series of Lie groups. Using the triality algebra, J. Landsberg and L. Manivel construct this Lie algebra in 2006. In this paper, we study the structure of following B. Gross and N. Wallach’s
Yongzhi Luan
semanticscholar   +1 more source

Doubly z-graded Lie algebras containing a Heisenberg algebra

Journal of Mathematical Sciences, 1999
A. Osborn, K. Zhao
exaly   +2 more sources