Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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01 Sep 1978
18 citations
TL;DR: In this article, the authors studied different qualitative properties of the semigroup generated by some degenerate differential elliptic operators on the standard simplex of R d and obtained the ultracontractivity property in the setting of weighted L p -spaces.
18 citations
18 citations
17 citations
TL;DR: In this article, the connection between amenability, Folner conditions and the geometry of finitely generated semigroups was studied, and it was shown that left amenability coincides with the strong Folner condition.
Abstract: We study the connection between amenability, Folner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left cancellative semigroups, finite semigroups, compact topological semigroups, inverse semigroups, regular semigroups, commutative semigroups and semigroups with a left, right or two-sided zero element), left amenability coincides with the strong Folner condition. Within the same class, we show that a finitely generated semigroup of subexponential growth is left amenable if and only if it is left reversible. We show that the (weak) Folner condition is a left quasi-isometry invariant of finitely generated semigroups, and hence that left amenability is a left quasi-isometry invariant of left cancellative semigroups. We also give a new characterisation of the strong Folner condition in terms of the existence of weak Folner sets satisfying a local injectivity condition on the relevant translation action of the semigroup.
17 citations