Abstract
In this chapter we show how monotone complete C ∗-algebras, of bounded cardinality, can be classified by a semigroup which we construct. We introduce the spectroid invariant for monotone \(\sigma\)-complete C ∗-algebras and show how it can also be defined for elements of the classification semigroup. In later chapters this theory will be applied to exhibit huge numbers of examples. We also indicate how aspects of this theory can be extended to more general classes of partially ordered set. We begin with a brief discussion of C ∗-algebras which are not “too large” and cardinalities.
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Saitô, K., Wright, J.D.M. (2015). Classification and Invariants. In: Monotone Complete C*-algebras and Generic Dynamics. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-6775-4_3
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DOI: https://doi.org/10.1007/978-1-4471-6775-4_3
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