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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...
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...
A global solution of Boltzmann equation is proposed after introducing a three-dimensional closed Lie group to simplify the collision term.
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...
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...
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 $\gg_2$. ...
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 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 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 -...
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。
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...
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...

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