Measures on the lattice of closed inner ideals in a spin triple
The structure of the complete lattice \(I(A)\) of closed inner ideals in a spin triple \(A\) and the measures on \(I(A)\), are studied in this paper. Let \(n\) be the dimension of \(A\). For \(n>5\), there are no non-zero measures on \(I(A)\). For \(n=5\), do exist measures on \(I(A)\), and, up to multiplication by a constant, a unique measure exists that is invariant under automorphisms of \(A\). For \(n=4\), \(A\) is isomorphic to the \(W^*\)-triple of \(2\times 2\) complex matrices. In this case, there is an uncountable number of measures on \(I(A)\).
scientific article; zbMATH DE number 1563085
scientific article