Relating homogeneous cones and positive definite cones via T-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(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 operat...
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| Format: | Article |
| Language: | English |
| Published: |
2009
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| Online Access: | https://hdl.handle.net/10356/90513 http://hdl.handle.net/10220/4702 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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