Word hyperbolic semigroups

Word Hyperbolic Semigroups 32

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...

Decision problems for word-hyperbolic semigroups

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...

Nonlinear 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 ...

Hyperbolic 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...