As it is well known, 20th century applied mathematics with related physical and chemical theories, are solely applicable to point-like particles moving in vacuum under Hamiltonian interactions (exterior dynamical problems). In this note, we study the covering of 20th century mathematics discovered by R. M. Santilli, today known as Santilli isomathematics, representing particles as being extended, non-spherical and deformable while moving within a physical medium under Hamiltonian and non-Hamiltonian interactions (interior dynamical problems). In particular, we focus the attention on a central part of isomathematics given by the isorepresentations of the Lie-Santilli isoalgebras that have been classified into regular (irregular) isorepresentations depending on whether the structure quantities of the isocommutation rules are constants (functions of local variables). The importance of the study of the isorepresentation theory for a number of physical and chemical applications is pointed out
| DOI | 10.11648/j.ajmp.s.2015040501.19 |
| Published in |
American Journal of Modern Physics (Volume 4, Issue 5-1, October 2015)
This article belongs to the Special Issue Issue I: Foundations of Hadronic Mathematics |
| Page(s) | 76-82 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Lie Theory, Lie-Santilli Isotheory, Isorepresentations
| [1] | R. M. Santilli, Foundation of Theoretical Mechanics, Volumes I (1978) [1a], and Volume II (1982) [1b], Springer-Verlag, Heidelberg, Germany, http://www.santilli-foundation.org/docs/Santilli-209.pdf http://www.santilli-foundation.org/docs/santilli-69.pdf |
| [2] | R. M. Santilli, "Isonumbers and Genonumbers of Dimensions 1, 2, 4, 8, their Isoduals and Pseudoduals, and "Hidden Numbers" of Dimension 3, 5, 6, 7," Algebras, Groups and Geometries Vol. 10, 273 (1993) http://www.santilli-foundation.org/docs/Santilli-34.pdf |
| [3] | R. M. Santilli, "Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures, P. Vetro Editor, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996) http://www.santilli-foundation.org/docs/Santilli-37.pdf |
| [4] | R. M. Santilli, JINR Rapid Comm. 6. 24-38 (1993), available as free download from http://www.santilli-foundation.org/docs/Santilli-19.pdf |
| [5] | R. M. Santilli, Acta Applicandae Mathematicae 50, 177 (1998), available as free download from http://www.santilli-foundation.org/docs/Santilli-19.pdf |
| [6] | R. M. Santilli, "Experimental Verifications of IsoRedShift with Possible Absence of Universe Expansion, Big Bang, Dark Matter, and Dark Energy," The Open Astronomy Journal 3, 124 (2010) http://www.santilli-foundation.org/docs/Santilli-isoredshift.pdf |
| [7] | R. M. Santilli, "Nuclear realization of hadronic mechanics and the exact representation of nuclear magnetic moments," R. M. Santilli, Intern. J. of Phys. Vol. 4, 1-70 (1998) http://www.santilli-foundation.org/docs/Santilli-07.pdf |
| [8] | R. M. Santilli, "Theoretical prediction and experimental verification of the new chemical species of magnecules," Hadronic J. 21, 789 (1998) http://www.santilli-foundation.org/docs/Santilli-43.pdf |
| [9] | R. M. Santilli, Elements of Hadronic Mechanics, Volumes I and II Ukraine Academy of Sciences, Kiev, 1995, http://www.santilli-foundation.org/docs/Santilli-300.pdf http://www.santilli-foundation.org/docs/Santilli-301.pdf |
| [10] | R. M. Santilli, Hadronic Mathematics, Mechanics and Chemistry,, Volumes I to V, International Academic Press, (2008), http://www.i-b-r.org/Hadronic-Mechanics.htm |
| [11] | R. M. Santilli, Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels, Kluwer Academic Publishers (2001), http: //www.santilli-foundation.org/docs/Santilli-113.pdf |
| [12] | H. Ahmar, G. Amato, J. V. Kadeisvili, J. Manuel, G. West, and O. Zogorodnia, "Additional experimental confirmations of Santilli’s IsoRedShift and the consequential expected absence of universe expansion," Journal of Computational Methods in Sciences and Engineering, 13, 321 (2013), http://www.santilli-foundation.org/docs/IRS-confirmations-212.pdf |
| [13] | Y. Yang, J. V. Kadeisvili, and S. Marton, "Experimental Confirmations of the New Chemical Species of Santilli Magnecules," The Open Physical Chemistry Journal Vol. 5, 1-16 (2013) http://www.santilli-foundation.org/docs/Magnecules-2012.pdf for the industrial realization of Santilli magnecules, please visit the website of the publicly traded U. S. company Magnegas Corporation www.magnegas.com |
| [14] | S. S. Dhondge, "Studies on Santilli Three-Body Model of the Deuteron According to Hadronic Mechanics," American Journal of Modern Physics, in press (2015) http://www.santilli-foundation.org/docs/deduteron-cpnfirm.pdf For the industrial realization of nuclear energies without harmful radiation, please visit the website of the publicly traded U. S. company Thunder Energies Corporation www.thunder-energies.comn |
| [15] | Chun-Xuan Jiang, Foundations of Santilli Isonumber Theory, International Academic Press (2001), http://www.i-b-r.org/docs/jiang.pdf |
| [16] | D. S. Sourlas and G. T. Tsagas, Mathematical Foundation of the Lie-Santilli Theory, Ukraine Academy of Sciences (1993) http://www.santilli-foundation.org/docs/santilli-70.pdf |
| [17] | J. V. Kadeisvili, "Foundations of the Lie-Santilli Isotheory," in "Isotopies of Contemporary Mathematical Structures," P. Vetro Editor, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996), http://www.santilli-foundation.org/docs/Santilli-37.pdf |
| [18] | R. M. Fal on and J. N. Valdés, Mathematical Foundations of Santilli Isotopies, Original monograph in Spanish published in 2001. The English translation has been published inAlgebras, Groups and Geometries Vol. 32, pages 135-308 (2015) http://www.i-b-r.org/docs/Aversa-translation.pdf |
| [19] | T. Vougiouklis, "The Santilli theory ’invasion’ in hyperstructures," Algebras, Groups and Geometries Vol. 28, pages 83-104 (2011) http://www.santilli-foundation.org/docs/santilli-invasion.pdf |
| [20] | S. Georgiev, Foundations of the IsoDifferential Calculus, Volumes I to V, Nova Scientific Publishers (2014 on ). |
| [21] | I. Gandzha and J. Kadeisvili, New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli, Sankata Printing Press, Nepal (2011), http://www.santilli-foundation.org/docs/RMS.pdf |
APA Style
Richard Anderson. (2015). Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras. American Journal of Modern Physics, 4(5-1), 76-82. https://doi.org/10.11648/j.ajmp.s.2015040501.19
ACS Style
Richard Anderson. Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras. Am. J. Mod. Phys. 2015, 4(5-1), 76-82. doi: 10.11648/j.ajmp.s.2015040501.19
AMA Style
Richard Anderson. Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras. Am J Mod Phys. 2015;4(5-1):76-82. doi: 10.11648/j.ajmp.s.2015040501.19
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Download@article{10.11648/j.ajmp.s.2015040501.19,
author = {Richard Anderson},
title = {Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras},
journal = {American Journal of Modern Physics},
volume = {4},
number = {5-1},
pages = {76-82},
doi = {10.11648/j.ajmp.s.2015040501.19},
url = {https://doi.org/10.11648/j.ajmp.s.2015040501.19},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2015040501.19},
abstract = {As it is well known, 20th century applied mathematics with related physical and chemical theories, are solely applicable to point-like particles moving in vacuum under Hamiltonian interactions (exterior dynamical problems). In this note, we study the covering of 20th century mathematics discovered by R. M. Santilli, today known as Santilli isomathematics, representing particles as being extended, non-spherical and deformable while moving within a physical medium under Hamiltonian and non-Hamiltonian interactions (interior dynamical problems). In particular, we focus the attention on a central part of isomathematics given by the isorepresentations of the Lie-Santilli isoalgebras that have been classified into regular (irregular) isorepresentations depending on whether the structure quantities of the isocommutation rules are constants (functions of local variables). The importance of the study of the isorepresentation theory for a number of physical and chemical applications is pointed out},
year = {2015}
}
TY - JOUR T1 - Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras AU - Richard Anderson Y1 - 2015/08/21 PY - 2015 N1 - https://doi.org/10.11648/j.ajmp.s.2015040501.19 DO - 10.11648/j.ajmp.s.2015040501.19 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 76 EP - 82 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.s.2015040501.19 AB - As it is well known, 20th century applied mathematics with related physical and chemical theories, are solely applicable to point-like particles moving in vacuum under Hamiltonian interactions (exterior dynamical problems). In this note, we study the covering of 20th century mathematics discovered by R. M. Santilli, today known as Santilli isomathematics, representing particles as being extended, non-spherical and deformable while moving within a physical medium under Hamiltonian and non-Hamiltonian interactions (interior dynamical problems). In particular, we focus the attention on a central part of isomathematics given by the isorepresentations of the Lie-Santilli isoalgebras that have been classified into regular (irregular) isorepresentations depending on whether the structure quantities of the isocommutation rules are constants (functions of local variables). The importance of the study of the isorepresentation theory for a number of physical and chemical applications is pointed out VL - 4 IS - 5-1 ER -
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