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Displaying 201 – 218 of 218

Tree algebras: An algebraic axiomatization of intertwining vertex operators

Igor Kříž, Yang Xiu (2012)

Archivum Mathematicum

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over $ℂ$ . We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over $ℚ$ .

Trees, free right-symmetric algebras, free Novikov algebras and identities.

Dzhumaldil'daev, Askar, Löfwall, Clas (2002)

Homology, Homotopy and Applications

Triangular Lie bialgebras and matched pairs for Lie algebras of real vector fields on $S^{1}$ .

Leitenberger, Frank (1994)

Journal of Lie Theory

Triple automorphisms of simple Lie algebras

Deng Yin Wang, Xiaoxiang Yu (2011)

Czechoslovak Mathematical Journal

An invertible linear map $ϕ$ on a Lie algebra $L$ is called a triple automorphism of it if $ϕ ([x, [y, z]]) = [ϕ (x), [ϕ (y), ϕ (z)]]$ for $\forall x, y, z \in L$ . Let $𝔤$ be a finite-dimensional simple Lie algebra of rank $l$ defined over an algebraically closed field $F$ of characteristic zero, $𝔭$ an arbitrary parabolic subalgebra of $𝔤$ . It is shown in this paper that an invertible linear map $ϕ$ on $𝔭$ is a triple automorphism if and only if either $ϕ$ itself is an automorphism of $𝔭$ or it is the composition of an automorphism of $𝔭$ and an extremal map of order $2$ .

Triple Cohomology of Lie Algebras

A. Patsourakos (1996)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Triple derivations on von Neumann algebras

Robert Pluta, Bernard Russo (2015)

Studia Mathematica

It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple) cohomological...

Troisième théorème fondamental de réalisation de Cartan

Ngô van Quê, A.A.M. Rodrigues (1975)

Annales de l'institut Fourier

De même qu’avec les groupes de Lie, à tout pseudo-groupe infinitésimal de Lie $θ$ sur $R^{n}$ il est associé de façon naturelle une algèbre de Lie $L (θ)$ , qui est une sous-algèbre de Lie fermée de l’algèbre de Lie $D$ de tous les champs de vecteurs formels de $R^{n}$ , l’algèbre $D$ étant munie de la topologie définie par la filtration naturelle de l’algèbre des séries formelles. Le troisième théorème fondamental de Cartan dit qu’inversement étant donnée une sous-algèbre de Lie transitive fermée $L$ de l’algèbre $D$ , il existe...

Twisted Hopf Algebras.

Rene Ruchti (1979)

Commentarii mathematici Helvetici

Twisted quantum doubles.

Fukuda, Daijiro, Kuga, Ken'ichi (2004)

International Journal of Mathematics and Mathematical Sciences

Twisted vertex representations of quantum affine algebras.

Naihuan Jing (1990)

Inventiones mathematicae

Twistor spinors and solutions of the equation (E) on Riemannian manifolds

Friedrich, Thomas, Pokorná, Olga (1991)

Proceedings of the Winter School "Geometry and Physics"

Two applications of elementary knot theory to Lie algebras and Vassiliev invariants.

Bar-Natan, Dror, Le, Thang T.Q., Thurston, Dylan P. (2003)

Geometry & Topology

Two classical results in the quantum mixed case.

Lars Thams (1993)

Journal für die reine und angewandte Mathematik

Two remarks on Lie rings of $2 \times 2$ matrices over commutative associative rings

Evgenii L. Bashkirov (2020)

Commentationes Mathematicae Universitatis Carolinae

Let $C$ be an associative commutative ring with 1. If $a \in C$ , then $a C$ denotes the principal ideal generated by $a$ . Let $l, m, n$ be nonzero elements of $C$ such that $m n \in l C$ . The set of matrices $(\begin{matrix} a_{11} & a_{12} a_{21} & - a_{11} \end{matrix})$ , where $a_{11} \in l C$ , $a_{12} \in m C$ , $a_{21} \in n C$ , forms a Lie ring under Lie multiplication and matrix addition. The paper studies properties of these Lie rings.

Currently displaying 201 – 218 of 218