UNSPECIFIED (1997) Cohomology of permutative cellular automata. ISRAEL JOURNAL OF MATHEMATICS, 99 . pp. 315-333. ISSN 0021-2172

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Abstract

We examine U(d) valued cocycles for a Z(2+) action generated by a mixing, permutative cellular automaton and show that the set of Holder continuous cocycles (for a given Holder order) which are cohomologous to constant cocycles is both open and closed in the appropriate topology. A continuous dimension function with values in {0, 1,..., d} is defined on cocycles; a cocycle is cohomologous to a constant precisely when the value is d. When d = 1 (the abelian case) the first (essential) cohomology group is countable. If U(1) congruent to circle is replaced by a finite subgroup, this cohomology group is finite.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ISRAEL JOURNAL OF MATHEMATICS
Publisher:	MAGNES PRESS
ISSN:	0021-2172
Date:	1997
Volume:	99
Number of Pages:	19
Page Range:	pp. 315-333
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/16416

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