Santilli Autotopisms of Partial Groups
American Journal of Modern Physics
Volume 4, Issue 5-1, October 2015, Pages: 47-51
Received: Jun. 8, 2015; Accepted: Jun. 15, 2015; Published: Aug. 11, 2015
Views 3880      Downloads 68
Authors
Raúl M. Falcón, Department of Applied Mathematics I, University of Seville, Seville, Spain
Juan Núñez, Department of Geometry and Topology, University of Seville, Seville, Spain
Article Tools
Follow on us
Abstract
This paper deals with those partial groups that contain a given Santilli isotopism in their autotopism group. A classification of these autotopisms is explicitly determined for partial groups of order n ≤ 4.
Keywords
Partial Group, Isotopism, Classification
To cite this article
Raúl M. Falcón, Juan Núñez, Santilli Autotopisms of Partial Groups, American Journal of Modern Physics. Special Issue: Issue I: Foundations of Hadronic Mathematics. Vol. 4, No. 5-1, 2015, pp. 47-51. doi: 10.11648/j.ajmp.s.2015040501.16
References
[1]
A. A. Albert, “Non-associative algebras. I. Fundamental concepts and isotopy,” Ann. of Math. 43:2, pp. 685–707, 1942.
[2]
R. H. Bruck, “Some results in the theory of linear non-associative algebras,” Trans. Amer. Math. Soc. 56, pp. 141–199, 1944.
[3]
R. M. Santilli, “On a possible Lie-admissible covering of the Galilei Relativity in Newtonian Mechanics for nonconservative and Galilei noninvariant systems,” Hadronic J. 1, pp. 223-423, 1978. Addendum, ibid 1, pp. 1279-1342, 1978.
[4]
R. M. Santilli, "Embedding of Lie algebras in Non-Associative Structures,” Nuovo Cimento 51, pp. 570-576, 1967.
[5]
R. M. Santilli, ''Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B 121, pp. 443-486, 2006.
[6]
P. Nikolaidou and T. Vougiouklis, “The Lie-Santilli admissible hyperalgebras of type An, “ Ratio Matematica 26, pp. 113-128, 2014.
[7]
J. V. Kadeisvili, “An introduction to the Lie-Santilli theory,” Acta Applicandae Mathematicae 50, pp. 131–165, 1998.
[8]
R. M. Falcón and J. Núñez, “Fundamentos de la isoteoría de Lie-Santilli,” International Academic Press, America-Europe-Asia, 2001.
[9]
R. M. Falcón, J. Núñez and A. Aversa, “Mathematical foundations of Santilli isotopies,” Algebras, Groups and Geometries 32, pp. 135-308, 2015.
[10]
R. M. Falcón and J. Núñez, “A particular case of extended isotopisms: Santilli's isotopisms", Hadronic J. 29:3, pp. 285-298, 2006.
[11]
R. M. Falcón and J. Núñez, “Partial Latin squares having a Santilli's autotopism in their autotopism groups,” J. Dyn. Syst. Geom. Theor. 5:1, pp. 19-32, 2007.
[12]
B. A. Hausmann and O. Ore, “Theory of Quasi-Groups,” Amer. J. Math. 59:4, pp. 983–1004, 1937.
[13]
A. A. Albert, “Quasigroups I,” Trans. Am. Math. Soc. 54, pp. 507-519, 1943.
[14]
A. A. Albert, “Quasigroups II,” Trans. Am. Math. Soc. 55, pp. 401-419, 1944.
[15]
R. H. Bruck, “Some results in the theory of quasigroups,” Trans. Amer. Math. Soc. 55, pp. 19–52, 1944.
[16]
B. D. McKay, A. Meynert, and W. Myrvold, “Small Latin squares, quasigroups, and loops,” J. Combin. Des. 15, pp. 98–119, 2007.
[17]
A. Hulpke, P. Kaski, and P. R. J. Östergard, “The number of Latin squares of order 11,” Math. Comp. 80, pp. 1197–1219, 2011.
[18]
R. M. Falcón, “The set of autotopisms of partial Latin squares”, Discrete Math. 313: 11, pp. 1150–1161, 2013.
[19]
R. M. Falcón, “Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method”, European J. Combin. 48, pp. 215–223, 2015.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186