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Meander graphs and Frobenius Seaweed Lie algebras
Meander graphs Frobenius Seaweed Lie algebras
2010/11/11
The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebr...
Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group
Dirac method symplectic submanifolds cotangent bundle factorizable Lie group
2010/11/18
In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these...
Equivariant K-theory for proper actions of non-compact Lie groups
Equivariant K-theory proper actions non-compact Lie groups
2010/11/8
Generalizing a construction of Wolfgang L\"uck and Bob Oliver, we define a good equivariant cohomology theory on the category of proper G-CW complexes when G is an arbitrary Lie group (possibly non-c...
Adjoint orbit types of compact exceptional Lie group G2 in its Lie algebra
exceptional Lie group G2 Lie algebra
2010/11/8
A Lie group $G$ naturally acts on its Lie algebra $\gg$, called the adjoint action. In this paper, we determine the orbit types of the compact exceptional Lie group $G_2$ in its Lie algebra $\gg_2$. ...
Lie group classifications and exact solutions for time-fractional Burgers equation
Lie group classifications exact solutions
2010/11/22
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-f...
We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classi...
The topology of a simple Lie group is essentially unique
topology simple Lie group essentially unique
2010/12/14
We study locally compact group topologies on simple Lie groups. We show that the Lie group topology on such a group S is very rigid: every ’abstract’ isomorphism between S and a locally compact and -...
Lee-Yang zeros for DHL and 2D rational dynamics, I. Foliation of the physical cylinder
Lee-Yang zeros DHL D rational dynamics I. Foliation of the physical cylinder
2010/12/10
In a classical work of the 1950’s, Lee and Yang proved that thezeros of the partition functions of a ferromagnetic Ising models always lie on the unit circle. Distribution of these zeros is physically...
Invariant generalized complex structures on Lie groups
Invariant generalized complex structures Lie groups
2010/11/30
We find an infinitesimal description of invariant generalized complex structures on Lie groups. We develop a systematic treatment of a class (called regular) of invariant generalized complex structure...
Some functional inequalities on polynomial volume growth Lie groups
Sobolev inequalities polynomial volume growth Lie groups
2010/12/7
We study in this article some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended without
the use of the Littlew...
Unitary representations of unimodular Lie groups in Bergman spaces
Unitary representations of unimodular Lie groups Bergman spaces
2010/12/3
For G an arbitrary unimodular Lie group, we construct strongly continuous unitary representations of G in the Bergman space of a naturally constructed strongly pseudoconvex neighborhood of the complex...
A classification theorem for Dirac homogeneous spaces of Dirac Lie groupoids
Poisson Lie groupoids Lie groupoids Dirac manifolds homogeneous spaces Courant algebroids
2010/11/29
The theorems in Drinfel′d (1993), Liu et al. (1998), Jotz (2010a) about one-one orrespondence between homogeneous objects of a Poisson Lie group (respectively Poisson Lie groupoid, Dirac Lie group)and...
An SKT metric is an Hermitian metric on a complex manifold whose fundamental 2-form ! satisfies @@! = 0. Streets and Tian introduced in [STb] a Ricci-type flow that preserves
the SKT condition.
Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups
existence of Einstein Ricci soliton metrics solvable Lie groups
2010/12/8
In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that ...
Linear Automorphism Groups of Relatively Free Groups
Linear Automorphism Groups Relatively Free Groups
2010/2/26
Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear if and only if G is a finitely generated virtually nilpotent group...