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The Jordan Algebraic Structure of the Circular Cone

Baha Alzalg (baha2math***at***gmail.com)

Abstract: In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The circular cones form a much more general class than the second-order cones, so we generalize some important algebraic properties in the Euclidean Jordan algebra of the second-order cones to the Euclidean Jordan algebra of the circular cones.

Keywords: Jordan algebras; Euclidean Jordan algebras; Symmetric cones; Circular cones; Second-order cones

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )


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Entry Submitted: 07/15/2015
Entry Accepted: 07/25/2015
Entry Last Modified: 12/05/2015

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