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The bounded spherical functions for the free two step nilpotent Lie group
nilpotent Lie group representation theory spherical function
2011/1/19
In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the action...
Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$
Exceptional Lie group Symmetric space
2011/2/21
For the simply connected compact exceptional Lie group E8, we determine the structure of subgroup (E8).
Smooth Lie group actions are parametrized diffeological subgroups
Smooth Lie group actions parametrized diffeological subgroups
2011/1/17
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset
diffeology of the functio...
Reduce and Solve Boltzmann Equation on a Global Lie Group
Reduce Solve Boltzmann Equation Global Lie Group
2011/1/21
A global solution of Boltzmann equation is proposed after introducing a three-dimensional closed Lie group to simplify the collision term.
The Freudenthal product and orbits in the Jordan algebra over the exceptional Lie group of type F$_{4(-20)}$
Freudenthal orbits Jordan algebra
2010/11/9
The orbit decomposition is presented for the real form of complex simple Jordan algebra with the automorphism group F$_{4(-20)}$, explicitly, in terms of the cross product and the characteristic polyn...
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...
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 $\gg_2$. ...
Orbit types of the compact Lie group E_7 in the complex Freudenthal vector space P^C
Lie group E_7 Freudenthal vector space P^C
2010/11/9
Let J be the exceptional Jordan algebra over R and J^C its complexification. Then the simply connected compact exceptional Lie group F_4 acts on J and F_4 has three orbit types which are F_4/F_4, F_4...
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...
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 -...
Convergence of semigroups of measures on a Lie group
Semigroups of measures dissipative distributions Hunt theory Lie groups
2010/12/9
A theorem of Siebert asserts that if μn(t) are semigroups of probability measures on a Lie group G, and Pn are the corresponding generating functionals,then μn(t).
An Example of Lie Group with Sasakian Structure of Constant $\Phi-$sectional Curvature
sasakian manifold lie group
2009/1/13
An Example of Lie Group with Sasakian Structure of Constant $\Phi-$sectional Curvature。
Expanded Lie group transformations
Lie group Lie algebra symmetry optimal system invariant
2010/9/14
Continuous groups of transformation acting on the expnded space of variables, which includes the equation parameters in addition to independent and dependent variables, are considered. It is shown tha...
Applications of Lie group analysis to the equations of motion of inclined unsagged cables
exact solutions inclined unsagged cables Lie group theory
2010/9/14
Analytical solutions to the equations of motion of inclined unsagged cables have been obtained by using the Lie group theory. The infinitesimal generators corresponding to the problem are calculated a...
Lie-group method for predicting water content for immiscible flow of two fluids in a porous medium
Lie-group method predicting water content immiscible flow of two fluids porous medium
2010/9/15
Lie-group method for predicting water content for immiscible flow of two fluids in a porous medium