In this paper, we classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. particular, our results cover Weyl–Hayashi algebra, quantization first algebra arising as primitive factor [Formula: see text], and family which localize to group infinite with generators text] subject relation

Let G ⩽ Sym ( Ω ) be a finite permutation group and recall that the base size of is minimal subset with trivial pointwise stabiliser. There an extensive literature on sizes for primitive groups, but there are very few results groups product type. In this paper, we initiate systematic study bases in setting. Our first main result determines every type form L ≀ P soluble point stabilisers, where ...

A uniformly recurrent pseudoword is an element of a free profinite semigroup in which every finite factor appears in every sufficiently long finite factor. An alternative characterization is as a pseudoword which is a factor of all its infinite factors, that is one which lies in a J -class with only finite words strictly J -above it. Such a J -class is regular and therefore it has an associated...

We consider various ways to represent irrational numbers by subrecursive functions. An irrational number can be represented by its base-b expansion; by its base-b sum approximation from below; and by its base-b sum approximation from above. Let S be a class of subrecursive functions, e.g., the class the primitive recursive functions. The set of irrational numbers that can be obtained by functio...