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arXiv · 2108.13078

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

Oleg Aristov
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Abstract

Dosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of Fr\'echet--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).

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Oleg Aristov. 2021-08-30. Sheaves of non-commutative smooth and holomorphic functions associated with the non-abelian two-dimensional Lie algebra. https://doi.org/10.1134/s0001434622070021

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