Journal of Lie Theory

no. 2
Hadamard Semigroups of Off-Diagonal Constant Matrices
Journal of Lie Theory, Volume 30 (2020) no. 2, pp. 473-488
The convex cone of positive semidefinite matrices of fixed size forms a commutative topological semigroup under the Hadamard product. In this paper we consider the closed subsemigroup of off-diagonal constant matrices, matrices having the same value in the off-diagonal positions, and its compact and convex subsemigroup of matrices with diagonal entries in the unit interval. Several results on these topological semigroups are presented: the group of units, (Loewner) ordered semigroup structures, one-parameter semigroups. An application of Hadamard powers obtained by FitzGerald and Horn and related open problems on Euclidean Jordan algebras are discussed.
DOI: 10.5802/jolt.1126
Classification: 22A20, 22A15, 15B48, 47L07
Keywords: Positive semidefinite matrix, Schur product theorem, Hadamard semigroup, off-diagonal constant matrix, topological semigroup, Loewner order, one-parameter semigroup, infinitely divisible matrix, Euclidean Jordan algebra, spin factor 
@article{JOLT_2020_30_2_a10,
     author = {Y. Lim},
     title = {Hadamard {Semigroups} of {Off-Diagonal} {Constant} {Matrices}},
     journal = {Journal of Lie Theory},
     pages = {473--488},
     year = {2020},
     volume = {30},
     number = {2},
     doi = {10.5802/jolt.1126},
     zbl = {1440.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1126/}
}
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%J Journal of Lie Theory
%D 2020
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%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1126/
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Y. Lim. Hadamard Semigroups of Off-Diagonal Constant Matrices. Journal of Lie Theory, Volume 30 (2020) no. 2, pp. 473-488. doi: 10.5802/jolt.1126

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