No abstract

We discuss a possible link between the deformation parameter μν arising in the framework of noncommutative geometry and the parameter β of the generalized uncertainty principle (GUP). We compute the shift of the Hawking temperature induced by the μν -deformed Schwarzschild geometry, and then we relate it to one obtained by GUP. Results suggest a granular structure of specetime at the Planck scales. The current bounds on β allow to constraint the noncommutative parameter μν .

n-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied.Necessary and sufficient conditions for the sum and the wedge product of two n-Poisson sructures to be again a multi-Poisson are found. It is proven that the canonical n-vector on the dual of an n-Lie algebra g is n-Poisson iff dim g ≤ n + 1.The problem of compatibility of two n-Lie algebra structures is analyzed and the compatibility relations connecting hereditary structures of a given n-Lie algebra are obtained. (n + 1)-dimensional n-Lie algebras are classified and their "elementary particle-like" structure is discovered.Some simple applications to dynamics are discussed.

Vacuum gravitational fields invariant for a bidimensional non Abelian Lie algebra of Killing fields, are explicitly described. They are parameterized either by solutions of a transcendental equation (the tortoise equation) or by solutions of a linear second order differential equation on the plane. Gravitational fields determined via the tortoise equation, are invariant for a 3-dimensional Lie algebra of Killing fields with bidimensional leaves. Global gravitational fields out of local ones are also constructed.