
Journal of Lie Theory 30 (2020), No. 2, 473488 Copyright Heldermann Verlag 2020 Hadamard Semigroups of OffDiagonal Constant Matrices Yongdo Lim Department of Mathematics, Sungkyunkwan University, Suwon 440746, Korea ylim@skku.edu 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 offdiagonal constant matrices, matrices having the same value in the offdiagonal 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, oneparameter semigroups. An application of Hadamard powers obtained by FitzGerald and Horn and related open problems on Euclidean Jordan algebras are discussed. Keywords: Positive semidefinite matrix, Schur product theorem, Hadamard semigroup, offdiagonal constant matrix, topological semigroup, Loewner order, oneparameter semigroup, infinitely divisible matrix, Euclidean Jordan algebra, spin factor. MSC: 22A20, 22A15, 15B48, 47L07. [ Fulltextpdf (146 KB)] for subscribers only. 