Finite fixed point algebras are subdiagonalisable
A fixed point algebra \(<A,B>\) consists of a Boolean algebra \(A\), together with a Boolean algebra \(B\) of functions on \(A\) which is closed under composition and where all the functions in \(B\) have a fixed point. The class of diagonalizable fixed point algebras was defined by Smoryński. It is shown that all finite fixed point algebras are subdiagonalizable, that is, of the form \(<A,C>\) where \(C\leq B\) and \(<A,B>\) is diagonalizable. It is also shown that a finite fixed point algebra is diagonalizable iff it is closed \((<A,B>\) is closed iff \(f\circ g\in B\) whenever \(f\in B\) and \(g\in Pol_1(A))\).
scientific article; zbMATH DE number 4019127
scientific article