Von Neumann regularity in Jordan triple systems

1972 ◽  
Vol 23 (1) ◽  
pp. 589-593 ◽  
Author(s):  
Kurt Meyberg
Keyword(s):  
Von Neumann ◽  
Triple Systems ◽  
Jordan Triple Systems

Primary Jordan triple systems. III

1985 ◽  
Vol 26 (1) ◽  
pp. 55-64 ◽  
Author(s):  
E. I. Zel'manov
Keyword(s):  
Triple Systems ◽  
Jordan Triple Systems

JORDAN SYMMETRIC SPACES

2009 ◽  
Vol 02 (03) ◽  
pp. 407-415
Author(s):  
Cho-Ho Chu
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Triple Systems ◽  
Infinite Dimensional ◽  
Jordan Triple Systems ◽  
Riemannian Symmetric Spaces

We introduce a class of Riemannian symmetric spaces, called Jordan symmetric spaces, which correspond to real Jordan triple systems and may be infinite dimensional. This class includes the symmetric R-spaces as well as the Hermitian symmetric spaces.

TERNARY ALGEBRAIC CONSTRUCTION OF EXTENDED SUPERCONFORMAL ALGEBRAS

1991 ◽  
Vol 06 (19) ◽  
pp. 1733-1743 ◽  
Author(s):  
MURAT GÜNAYDIN ◽  
SEUNGJOON HYUN
Keyword(s):  
Lie Groups ◽  
Symmetric Spaces ◽  
Coset Space ◽  
Algebraic Construction ◽  
Hermitian Symmetric Spaces ◽  
Magic Square ◽  
Triple Systems ◽  
Coset Spaces ◽  
Jordan Triple Systems ◽  
Ternary Algebras

We give a construction of extended (N = 2 and N = 4) superconformal algebras over a very general class of ternary algebras (triple systems). For N = 2 this construction leads to superconformal algebras corresponding to certain coset spaces of Lie groups with non-vanishing torsion and generalizes a previous construction over Jordan triple systems which are associated with Hermitian symmetric spaces. In general, a given Lie group admits more than one coset space of this type. We give examples for all simple Lie groups. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU (2) × SU (2) × U (1). We give a complete list of the FT systems and the corresponding N = 4 models. They are associated with the unique quaternionic symmetric spaces of Lie groups.

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