2023/05/30 by Onno van Gaans, van Gaans, Onno, Anke Kalauch +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B40 #Rough Sets and Fuzzy Logic #Secondary 17C65
paper · pdf · doi:10.48550/arxiv.2305.19086
openalex publication_date 2023/05/30 · openalex created_date 2023/06/01 · openalex updated_date 2026/07/28
Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison's anti-lattice theorem, we show that each of these factors is a disjointness free anti-lattice. We characterise disjointness, bands, and disjointness preserving bijections with disjointness preserving inverses in direct sums of disjointness free anti-lattices and, therefore, in atomic JBW-algebras. We show that in unital JB-algebras the algebraic centre and the order theoretical centre are isomorphic. Moreover, the order theoretical centre is a Riesz space of multiplication operators. A survey of JBW-algebra factors of type I is included.