TY - JOUR
T1 - Realization of homogeneous cones through oriented graphs
AU - Yamasaki, Takashi
AU - Nomura, Takaaki
N1 - Publisher Copyright:
© 2015 Faculty of Mathematics, Kyushu University.
PY - 2015
Y1 - 2015
N2 - In this paper, we realize any homogeneous cone by assembling uniquely determined subcones. These subcones are realized in the cones of positive-definite real symmetric matrices of minimal possible sizes. The subcones are found through the oriented graphs drawn by using the data of the given homogeneous cones. We also exhibit several interesting examples of our realizations of homogeneous cones. These are of rank 5, of dimension 19, of dimension 11 of continuously many inequivalent homogeneous cones, and some of the low-dimensional homogeneous cones.
AB - In this paper, we realize any homogeneous cone by assembling uniquely determined subcones. These subcones are realized in the cones of positive-definite real symmetric matrices of minimal possible sizes. The subcones are found through the oriented graphs drawn by using the data of the given homogeneous cones. We also exhibit several interesting examples of our realizations of homogeneous cones. These are of rank 5, of dimension 19, of dimension 11 of continuously many inequivalent homogeneous cones, and some of the low-dimensional homogeneous cones.
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U2 - 10.2206/kyushujm.69.11
DO - 10.2206/kyushujm.69.11
M3 - Article
AN - SCOPUS:84930977695
SN - 1340-6116
VL - 69
SP - 11
EP - 48
JO - Kyushu Journal of Mathematics
JF - Kyushu Journal of Mathematics
IS - 1
ER -