相关论文: General Formulas of the Structure Constants in the…
The standard way to compute the structure constants of semi-simple Lie algebras involves the additive structure of the roots. In earlier work, I described how ideas of Jacques Tits could be applied to do this by using the structure of the…
Explicit structure constants are calculated for certain Lie algebras of vectorfields on 2-dimensional compact manifolds.
he analytic formulas for structure constants of $su(2S+1)$ algebra in terms of $3jm$ and $6j$ symbols of $su(2)$ have been derived for the decomplexification of the Liouville-von Neumann equation.
Libor \v{S}nobl and Pavel Winternitz classified all of the Lie algebras of dimension six and smaller. Using this classification, we formulated and proved structure constant formulas for the universal enveloping algebras of the nilpotent Lie…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
This article is the second in the series and is devoted to the type G_2. The work consists of two parts. In the first part we calculate the structure constants of the complex simple Lie algebra of type G_2. All structure constants are…
We present the structural constants of low dimensional pseudo $H$-type algebras.
We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.
The structure constants $N_{\lambda, \mu}^{\mu+\nu}$ of the $sl_2$ Verlinde algebra as functions of $\mu$ either vanish or can be expressed after a change of variable as the weight function of an irreducible representation of $sl_2$. We…
We show that the structure constants of $k$-Lie algebras, $k>3$, with a positive definite metric are the sum of the volume forms of orthogonal $k$-planes. This generalizes the result for $k=3$ in arXiv:0804.2662 and arXiv:0804.3078, and…
We study post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic…
A closed formula for the structure constants in the SL(2,C)/SU(2) WZNW model is derived by a method previously used in Liouville theory. With the help of a reflection amplitude that follows from the structure constants one obtains a…
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U(N_+,N_-) are provided. They generalize the Virasoro and W_\infty algebras to higher dimensions. The…
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in $h$. They are derived from the quantized enveloping algebras $\uqg$. The quantum Lie bracket satisfies a generalization of antisymmetry.…
The purpose of this paper is to answer the question whether it is possible to realize simultaneously the relations $N_{\alpha,\beta}=-N_{-\alpha,-\beta}$, $N_{\alpha,\beta}=N_{\beta,-\alpha-\beta}=N_{-\alpha-\beta,\alpha}$ and…
For a simple complex Lie algebra $\mathfrak{g}$, fixing a principal $\mathfrak{sl}_2$-triple and highest weight vectors induces a basis of $\mathfrak{g}$ as vector space. For $\mathfrak{sl}_n$, we describe how to compute the Lie bracket in…
This article is the third in the series. It is devoted the calculation of the structure constants for the complex simple Lie algebra of type E_6 and Chevalley commutator formulas.
Given a $n$-dimensional Lie algebra $g$ over a field $k \supset \mathbb Q$, together with its vector space basis $X^0_1,..., X^0_n$, we give a formula, depending only on the structure constants, representing the infinitesimal generators,…
We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…