scholarly journals Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras

1999 ◽  
Vol 59 (2) ◽  
pp. 187-201
Author(s):  
Sang Youl Lee ◽  
Yongdo Lim ◽  
Chan-Young Park

In this article we define symmetric geodesies on conformal compactifications of Euclidean Jordan algebras and classify symmetric geodesics for the Euclidean Jordan algebra of all n × n symmetric real matrices. Furthermore, we show that the closed geodesics for the Euclidean Jordan algebra of all 2 × 2 symmetric real matrices are realised as the torus knots in the Shilov boundary of a Lie ball.

2021 ◽  
Vol 37 (37) ◽  
pp. 156-159
Author(s):  
Jiyuan Tao

In a recent paper [Linear Algebra Appl., 461:92--122, 2014], Tao et al. proved an analog of Thompson's triangle inequality for a simple Euclidean Jordan algebra by using a case-by-case analysis. In this short note, we provide a direct proof that is valid on any Euclidean Jordan algebras.


2013 ◽  
Vol 15 (04) ◽  
pp. 1340034 ◽  
Author(s):  
JIYUAN TAO ◽  
M. SEETHARAMA GOWDA

A Lyapunov-like (linear) transformation L on a Euclidean Jordan algebra V is defined by the condition [Formula: see text]where K is the symmetric cone of V. In this paper, we give an elementary proof (avoiding Lie algebraic ideas and results) of the fact that Lyapunov-like transformations on V are of the form La + D, where a ∈ V, D is a derivation, and La(x) = a ◦ x for all x ∈ V.


2012 ◽  
Vol 29 (02) ◽  
pp. 1250015 ◽  
Author(s):  
G. Q. WANG

In this paper, we present a new polynomial interior-point algorithm for the monotone linear complementarity problem over symmetric cones by employing the framework of Euclidean Jordan algebras. At each iteration, we use only full Nesterov and Todd steps. The currently best known iteration bound for small-update method, namely, [Formula: see text], is obtained, where r denotes the rank of the associated Euclidean Jordan algebra and ε the desired accuracy.


4open ◽  
2019 ◽  
Vol 2 ◽  
pp. 21
Author(s):  
Luís Vieira

Let G be a primitive strongly regular graph G such that the regularity is less than half of the order of G and A its matrix of adjacency, and let 𝒜 be the real Euclidean Jordan algebra of real symmetric matrices of order n spanned by the identity matrix of order n and the natural powers of A with the usual Jordan product of two symmetric matrices of order n and with the inner product of two matrices being the trace of their Jordan product. Next the spectra of two Hadamard series of 𝒜 associated to A2 is analysed to establish some conditions over the spectra and over the parameters of G.


2009 ◽  
Vol 430 (8-9) ◽  
pp. 1992-2011 ◽  
Author(s):  
M. Seetharama Gowda ◽  
Jiyuan Tao ◽  
Melania Moldovan

1992 ◽  
Vol 07 (15) ◽  
pp. 3623-3637 ◽  
Author(s):  
R. FOOT ◽  
G. C. JOSHI

It is shown that the sequence of Jordan algebras [Formula: see text], whose elements are the 3 × 3 Hermitian matrices over the division algebras ℝ, [Formula: see text], ℚ and [Formula: see text], can be associated with the bosonic string as well as the superstring. The construction reveals that the space–time symmetries of the first-quantized bosonic string and superstring actions can be related. The bosonic string and the superstring are associated with the exceptional Jordan algebra while the other Jordan algebras in the [Formula: see text] sequence can be related to parastring theories. We then proceed to further investigate a connection between the symmetries of supersymmetric Lagrangians and the transformations associated with the structure group of [Formula: see text]. The N = 1 on-shell supersymmetric Lagrangians in 3, 4 and 6-dimensions with a spin 0 field and a spin 1/2 field are incorporated within the Jordan-algebraic framework. We also make some remarks concerning a possible role for the division algebras in the construction of higher-dimensional extended objects.


2019 ◽  
Vol 72 (1) ◽  
pp. 183-201 ◽  
Author(s):  
Marcela Hanzer ◽  
Gordan Savin

AbstractWe describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.


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