An introduction to the Lie-Santilli theory
type: Item
instance of: scholarly article
title: An introduction to the Lie-Santilli theory
zbMATH Open document ID: 0902.53050
DOI: 10.1023/A:1005827519994
author: J. V. Kadeisvili
published in: Acta Applicandae Mathematicae
publication date: 1998-12-13T00:00:00Z
review text: One of the most visible differences in the transition from special relativity with the Minkowskian line element \[ ds^2= dx^\mu \eta_{\mu\nu} dx^\nu, \quad \eta= \text{diag} (1, 1, 1,-1), \quad x=(x, c_0t), \] to general relativity for the exterior gravitational problem in vacuum with the Riemannian line element \(ds^2= dx^\mu g_{\mu\nu} (x)dx^\nu\) is that the former is reducible to the primitive Poincaré symmetry P(3.1), while the latter is not believed to be reducible to a single symmetry. The problem has been solved by R. Santilli using isostructure theory. This paper presents the methodology for the solution of this problem. The section headings are the following: (i) symmetries of exterior gravitation, (ii) symmetries of interior gravitation, (iii) bibliographical notes, (iv) isotopies and isodualities of the unit, (v) isotopies and isodualities of fields, (vi) isospaces and their isoduals, (vii) isotopies and isodualities of the transformation theory, (iix) isotopies and isodualities of functional analysis, (ix) isotopies and isodualities for universal enveloping associative algebras, (x) isotopies and isodualities of Lie algebras, (xi) isotopies and isodualities of Lie groups, (xii) the fundamental theorem on isosymmetries, (xiii) isotopies and isodualities of the rotational symmetry, (xv) isotopies and isodualities of the Lorentz and Poincaré symmetries, (xiv) mathematical and physical applications.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 57R52
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 83C40
zbMATH DE Number: 1139656
zbMATH Keywords: Santilli's isotopies
zbMATH Keywords: isospaces
zbMATH Keywords: isodualities
zbMATH Keywords: universal enveloping associative algebras
zbMATH Keywords: Lie algebras
zbMATH Keywords: symmetries in general relativity
reviewed by: Grigorios Tsagas
MaRDI profile type: Publication
full work available at URL: a:1005827519994
OpenAlex ID: W2914556153
Recommended article: Q4717974
Recommended article: Q4331547
Recommended article: Q4840683
Recommended article: Q4365108
Recommended article: Q4347834
Recommended article: An introduction to string Lie theory
Recommended article: Q3692519
Recommended article: Q5472809
Recommended article: Q4841400
Recommended article: Q5565746
description: scientific article; zbMATH DE number 1139656