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Representations for the restricted Lie color algebras
Representations the restricted Lie color algebras
2010/11/12
The generalized p-characters for the restricted Lie color are defined. The simplicity of the induced modules for the FP triples are determined. As applications, we have obtained an analogue of the Ka...
The (G, \theta)-Lie algebras are structures which unify the Lie algebras and Lie superalgebras. We use them to produce solutions for the quantum Yang-Baxter equation. The constant and the spectral-par...
Lie-Hopf algebras and loop homology of suspension spaces
Lie-Hopf algebras loop homology suspension spaces
2010/11/18
For an arbitrary topological space $X$, the loop space homology $H_*(\Omega\Sigma X; \mathbb{Z})$ is a Hopf algebra. We introduce a new homotopy invariant of a topological space $X$ that takes values...
A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities
Lie algebraic Ricci flow invariant curvature conditions Harnack inequalities
2010/11/22
We consider a subset $S$ of the complex Lie algebra $\so(n,\C)$ and the cone $C(S)$ of curvature operators which are nonnegative on $S$. We show that $C(S)$ defines a Ricci flow invariant curvature co...
Vertex Operator Algebras Associated to Type G Affine Lie Algebras
Vertex Operator Algebras Associated Type G Affine Lie Algebras
2010/11/22
In this paper, we study representations of the vertex operator algebra $L(k,0)$ at one-third admissible levels $k= -5/3, -4/3, -2/3$ for the affine algebra of type $G_2^{(1)}$. We first determine sin...
In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D...
Classification of Harish-Chandra modules over some Lie algebras and superconformal algebras related to the Virasoro algebra
Harish-Chandra modules Lie algebras
2010/11/22
In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras and superconformal algebras related to the Virasoro algebras. We first classify suc...
Lipschitz retraction and distortion for subgroups of Out(F_n)
Lipschitz retraction distortion subgroups of Out(F_n)
2010/12/13
Given a finitely generated group G, a finitely generated subgroup H is undistorted in G if the inclusion map H →֒ G is a quasi-isometric embedding with respect to word metrics. Nondistortion may...
On cohomology and support varieties for Lie superalgebras
cohomology varieties Lie superalgebras
2010/12/8
Support varieties for Lie superalgebras over the complex numbers were introduced in [BKN1] using the relative cohomology. In this paper we discuss finite generation of the relative cohomology rings fo...
Automorphism group and ad-invariant metric on all six dimensional solvable real Lie algebras
Automorphism group ad-invariant metric all six dimensional solvable real Lie algebras
2010/11/30
Using adjoint representation of Lie algebras, we calculate the automorphism group and ad-invariant metric on six dimensional solvable real Lie algebras with 5, 4 and 3 dimensional nilradicals.
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
Formality Deformation Quantization Operads
2010/12/1
We show that the zeroth cohomology of Kontsevich’s graph complex is isomorphic to the Grothendieck-Teichm¨uller Lie algebra grt. The map is explicitly described.
Inner Automorphisms of Lie Algebras Related with Generic 2 x 2 Matrices
free Lie algebras generic matrices inner automorphisms
2010/12/13
Let Fm = Fm(varsl2(K)) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl2(K) over a field K of characteristic 0.
Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms
Hom-Lie algebra representation quadratic form quadratic Hom-Lie algebra
2010/12/9
The aim of this paper is to introduce and study quadratic Hom-Lie algebras, which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. We provide several onstructions
leading t...
The Dixmier map for nilpotent super Lie algebras
Dixmier map Kirillov orbit method Lie superalgebras representation theory
2010/11/30
In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by Prim(U(g)) the set of (graded) primitive ideals of the enveloping algebra U(g...
Irregular locus of the commuting variety of reductive symmetric Lie algebras and rigid pairs
Irregular locus of the commuting variety reductive symmetric Lie algebras and rigid pairs
2010/11/29
The aim of this paper is to describe the irregular locus of the commuting variety of a reductive symmetric Lie algebra. More precisely, we want to enlighten a remark of Popov. In [Po], the irregular l...