Relating homogeneous cones and positive definite cones via T-algebras.
Chua, Chek Beng.
Date of Issue2003
School of Physical and Mathematical Sciences
T-algebras are nonassociative algebras defined by Vinberg in the early 1960s for the purpose of studying homogeneous cones. Vinberg defined a cone K(A) for each T-algebra A and proved that every homogeneous cone is isomorphic to one such K(A). We relate each T-algebra A with a space of linear operators in such a way that K(A) is isomorphic to the cone of positive definite self-adjoint operators. Together with Vinberg’s result, we conclude that every homogeneous cone is isomorphic to a “slice” of a cone of positive definite matrices.
SIAM Journal on Optimization.
SIAM Journal on Optimization @ copyright 2003 The journal's website is located at http://www.siam.org/journals/siopt.php.