In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

A low complexity Lie group method for numerical integration of ordinary differential equations on the orthogonal Stiefel manifold is presented. Based on the quotient space representation of the Stiefel manifold we provide a representation of the tangent space suitable for Lie group methods. According to this representation a special type of generalized polar coordinates (GPC) is defined and use...

For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of SU(2) and construct the number-type eigenstates and the coherent states using the spectrum-generating Lie algebra of SU(1, 1). We obtain the evolution operator in both of the Lie algebras. The number-type eigenstates and the coherent states are constructed g...

We classify realizations of the Lie algebras of the rotation O(3) and Euclid E(3) groups within the class of first-order differential operators in arbitrary finite dimensions. It is established that there are only two distinct realizations of the Lie algebra of the group O(3) which are inequivalent within the action of a diffeomorphism group. Using this result we describe a special subclass of ...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

Given a close 3-form H ∈ Ω 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω 0 (M). We define the group of H-twisted Hamiltonian symmetries Ham(M, J;H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which leads to generalized complex reduction much the same way as symplectic reduction is constructed. The definitions a...

Let → Γ be a valued quiver. Let C be the symmetrizable generalized Cartan matrix associated to → Γ. We show that the whole quantum group associated to C can be realized from the category of the representations of the product valued quiver → Γ. This method can be used to realize the whole generalized Kac-Moody Lie algebra associated to C, as discussed in [LL].

Generalized affine Grassmannian slices provide geometric realizations for weight spaces of representations semisimple Lie algebras. They are also Coulomb branches, symplectic dual to Nakajima quiver varieties. In this paper, we prove that neighboring generalized related by Hamiltonian reduction the action additive group. We a weaker version same result their quantizations, algebras known as tru...