Finite fixed point algebras are subdiagonalisable
type: Item
instance of: scholarly article
title: Finite fixed point algebras are subdiagonalisable
zbMATH Open document ID: 0627.06013
DOI: 10.1007/BF01229971
author: David Hobby
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: 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 \(g\in Pol_1(A))\).
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 06E30
Mathematics Subject Classification ID: 03G05
zbMATH DE Number: 4019127
zbMATH Keywords: Boolean algebra
zbMATH Keywords: diagonalisable fixed point algebras
zbMATH Keywords: finite fixed point algebras
zbMATH Keywords: subdiagonalisable
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01229971
OpenAlex ID: W2033024480
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description: scientific article; zbMATH DE number 4019127