caa a22 4500 397532814 CHVBK 20180308164656.0 cr unu---uuuuu 161202e199502 xx s 000 0 eng 10.1112/jlms/51.1.148 doi (NATIONALLICENCE)oxford-10.1112/jlms/51.1.148 Decomposability of Reflexive Cycle Algebras [Elektronische Daten] [K.J. Harrison, U.A. Mueller] We give, for each n ≥ 3, an example of a reflexive operator algebra 𝒜n with the following properties: (i) each finite rank operator with rank less than n - 1 is the sum of rank-one operators in 𝒜n, and (ii) there is an operator of rank n - 1 in 𝒜n which is not the sum of rank-one operators in 𝒜n. The invariant subspace lattice of 𝒜n is finite and distributive with 2n join-irreducible elements. We show also that the indecomposability of 𝒜n is related to the existence of a chordless cycle in a bipartite graph associated with 𝒜n. © The London Mathematical Society Notes and Papers nationallicence Harrison K.J. Mathematics Department, Murdoch University Murdoch, Western Australia 6150, Australia E-mail: harrison@csuvaxl.murdoch.edu.au aut Mueller U.A. Department of Mathematics, Edith Cowan University Perth, Western Australia 6050, Australia E-mail: u.mueller@cowan.edu.au aut Journal of the London Mathematical Society Oxford University Press 51/1(1995-02), 148-160 0024-6107 51:1<148 1995 51 jlms https://doi.org/10.1112/jlms/51.1.148 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1112/jlms/51.1.148 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Harrison K.J. Mathematics Department, Murdoch University Murdoch, Western Australia 6150, Australia E-mail: harrison@csuvaxl.murdoch.edu.au aut NATIONALLICENCE 700 1- Mueller U.A. Department of Mathematics, Edith Cowan University Perth, Western Australia 6050, Australia E-mail: u.mueller@cowan.edu.au aut NATIONALLICENCE 773 0- Journal of the London Mathematical Society Oxford University Press 51/1(1995-02), 148-160 0024-6107 51:1<148 1995 51 jlms Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford