The algebra of the generators of translations in superspace is unstable, in the sense that infinitesimal perturbations of its structure constants lead to non-isomorphic algebras. We show how superspace extensions remedy this situation (after arguing that remedy is indeed needed) and review the benefits reaped in the description of branes of all kinds in the presence of the extra dimensions. 1 C...

In this paper we prove sufficient conditions for the existence of global solutions of nonlinear functional-differential evolution equations whose linear parts are infinitesimal generators of strongly continuous and analytic semigroups. We apply the obtained results to a diffusion problem. 2000 MSC: Primary: 47J35, 34K12, Secondary: 34K90, 35K20, 35K60

Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. For that we elaborate on the reinterpretation of Cartan’s moving frame by Fels and Olver (1999). This provides constructive tools for exploring algebras of differential invariants.

Abstract In this paper, we concentrate on the Lie symmetry structure of a system multi-dimensional time-fractional partial differential equations (PDEs). Specifically, first give an explicit prolongation formula involving Riemann–Liouville derivative for infinitesimal generator in case, and then show that has elegant structure. Furthermore, present two simple conditions to determine generators ...

A logarithm representation of evolution operators is defined. Generators of invertible evolution families are characterized by the logarithm representation. In this article, using the logarithm representation, a concept of evolution operators without satisfying the semigroup property is introduced. In conclusion the existence of alternative infinitesimal generator is clarified.

The infinitesimal generators of Lévy processes in Euclidean space are pseudo-differential operators with symbols given by the Lévy-Khintchine formula. This classical analysis relies heavily on Fourier analysis which in the case when the state space is a Lie group becomes much more subtle. Still the notion of pseudo-differential operators can be extended to connected, simply connected nilpotent ...

We study nonlinear semigroups of holomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog of the Hille exponential formula. We then apply our results to the null point theory of semi-plus complete vector fields. We study the structure of null point set...