Basic concepts on Lorentz simmetry and Minkowsky isogeometry by using the MCIM isotopic model

Abstract

At 1978, R.M. Santilli proposed to generalize the conventional Lie theory by using isotopies. To do it, he considered that the basic unit of any mathematical structure can depend on external factors (such as positions, speed, acceleration, time, temperature or density: Î = Î (x, x*, xx**, …, µ, τ, …). In this way, Santilli obtains a more general Lie theory, based on nonassociative, nonlinear and non-local integral systems, which allows him to identify between themselves Euclidean, Riemannian and Minkowskian spaces, when working with extended particles or high energies into unusual physical conditions in exterior or interior dynamic systems. In the 80’s and 90’s, several mathematicians and physicits have investigated on Lie-Santilli’s theory. Particularly, Lorentz symmetry and Minkowski isogeommetry have been studied by Santilli and A.K. Aringazin in the 90’s. We propose to revise some of these concepts by using the MCM isotopic model studied at 2001. So, we will need to generalize the construction of isovectorspaces and the isodifferential calculus.