منابع مشابه
2 Word Hyperbolic Semigroups
The study of automatic and word hyperbolic groups is a prominent topic in geometric group theory. The definition of automatic groups extends naturally to semigroups [3, 8], but word hyperbolic groups are defined by a geometric condition, the thin triangle condition, whose extension is not immediate. The problem is that for semigroups the metric properties of the Cayley diagram are not as closel...
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This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan &Gilman. A fundamental investigation reveals that the natural definition of a ‘word-hyperbolic structure’ has to be strengthened slightly in order to define a unique semigroup up to isomorphism. The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the...
متن کاملNonlinear semigroups and a hyperbolic conservation law
This paper is concerned with the hyperbolic conservation law M i\ Sxa . db(u) _ St + ^ x ^ ~ ° (1.2) u(x,O) = f (x) . By means of the Crandall-Liggett theory of nonlinear semigroups ([1]), it will be shown that the operator A : u H-> ——b(u) Q. X generates a semigroup S = {Sfc; t ;> 0} of contraction operators on L (IR). The function t h-» S.f may then be thought of as a generalized solution of ...
متن کاملHyperbolic Groups and Completely Simple Semigroups
We begin with a brief introduction to the theory of word hyperbolic groups. We then consider four possible conditions which might reasonably be used as definitions or partial definitions of hyperbolicity in semigroups: having a hyperbolic Cayley graph; having hyperbolic Schützenberger graphs; having a context-free multiplication table; or having word hyperbolic maximal subgroups. Our main resul...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2004
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004103007497