Geodesic
Sheaves of Noncommutative Smooth and Holomorphic Functions Associated with the Non-Abelian Two-Dimensional Lie Algebra
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 20-30

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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).
Keywords: function of noncommuting variables, smooth function, holomorphic function, Lie algebra, sheaf of noncommutative algebras. 
@article{MZM_2022_112_1_a1,
     author = {O. Yu. Aristov},
     title = {Sheaves of {Noncommutative} {Smooth} and {Holomorphic} {Functions} {Associated} with the {Non-Abelian} {Two-Dimensional} {Lie} {Algebra}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {20--30},
     publisher = {mathdoc},
     volume = {112},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a1/}
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O. Yu. Aristov. Sheaves of Noncommutative Smooth and Holomorphic Functions Associated with the Non-Abelian Two-Dimensional Lie Algebra. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 20-30. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a1/