Studies of the Regular and Irregular Isorepresentations of the Lie-Santilli IsotheoryMuktibodh AS1* and Santilli RM2
- *Corresponding Author:
- Muktibodh AS
Institute for Basic Research
Palm Harbor, Florida, USA
Tel: +1-727-688 3992
E-mail: [email protected]
Received Date: March 12, 2017; Accepted Date: April 13, 2017; Published Date: April 17, 2017
Citation: Muktibodh AS, Santilli RM (2017) Studies of the Regular and Irregular Isorepresentations of the Lie-Santilli Isotheory. J Generalized Lie Theory Appl 11: 251. doi: 10.4172/1736-4337.1000251
Copyright: © 2017 Muktibodh AS, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
As it is well known, the Lie theory is solely applicable to dynamical systems consisting of point-like particles moving in vacuum under linear and Hamiltonian interactions (systems known as exterior dynamical systems). One of the authors (R.M. Santilli) has proposed an axiom-preserving broadening of the Lie theory, known as the Lie-Santilli isotheory, that is applicable to dynamical; systems of extended, non-spherical and deformable particles moving within a physical medium under Hamiltonian as well as non-linear and non-Hamiltonian interactions (broader systems known as interior dynamical systems). In this paper, we study apparently for the first time regular and irregular isorepresentations of Lie-Santilli isoalgebras occurring when the structure quantities are constants or functions, respectively. A number of applications to particle and nuclear physics are indicated. It should be indicated that this paper is specifically devoted to the study of isorepresentations under the assumption of a knowledge of the Lie-Santilli isotheory, as well as of the isotopies of the various branches of 20th century applied mathematics, collectively known as isomathematics, which is crucial for the consistent formulation and elaboration of isotheories.