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Relating Homogeneous Cones and Positive Definite Cones via <i>T</i>-Algebras
T-algebras are nonassociative algebras defined by Vinberg in the early 1960s for the purpose of studying homogeneous cones. Vinberg defined a cone $K({\cal A})$ for each T-algebra ${\cal A}$ and proved that every homogeneous cone is isomorphic to one such $K({\cal A})$. We relate each T-algebra ${\cal A}$ with a …