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Cohomology of permutative cellular automata
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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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ISRAEL JOURNAL OF MATHEMATICS | ||||
Publisher: | MAGNES PRESS | ||||
ISSN: | 0021-2172 | ||||
Official Date: | 1997 | ||||
Dates: |
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Volume: | 99 | ||||
Number of Pages: | 19 | ||||
Page Range: | pp. 315-333 | ||||
Publication Status: | Published |
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