Sheaves of non-commutative smooth and holomorphic functions associated with the non-abelian two-dimensional Lie algebra

Abstract

Dosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of Fréchet--Arens--Michael algebras (of noncommutative holomorphic functions in the complex case and of noncommutative smooth functions in the real case). We construct similar sheaves (both versions, holomorphic and smooth) on a special space of representations for the Lie algebra of the group of affine transformations of the real line (which is the simplest nonnilpotent solvable Lie algebra).

arXiv commentversion 5: English translation (by Math. Notes), version 4 and earlier in Russian, version 3: correction in Th.1.2, version 2: correction in Th.2.1