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Abstract.
A cone K is called homogeneous if for any two points x and y
in K there exists a non-degenerate linear automorphism A of K (i.e.
AK=K) such that Ax=y. Homogeneous cones were partially classified in
terms of T-algebras by Vinberg. He proved that each homogeneous cone is
isomorphic to a cone of generalized positive-definite Hermitian
matrices. In the talk, we will present key results that lead to this
classification, introduce T-algebras, and talk about applications in
the interior-point theory for convex programming problems. |