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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - O. Yu. Aristov
TI  - Sheaves of Noncommutative Smooth and Holomorphic Functions Associated with the Non-Abelian Two-Dimensional Lie Algebra
JO  - Matematičeskie zametki
PY  - 2022
SP  - 20
EP  - 30
VL  - 112
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a1/
LA  - ru
ID  - MZM_2022_112_1_a1
ER  - 
%0 Journal Article
%A O. Yu. Aristov
%T Sheaves of Noncommutative Smooth and Holomorphic Functions Associated with the Non-Abelian Two-Dimensional Lie Algebra
%J Matematičeskie zametki
%D 2022
%P 20-30
%V 112
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a1/
%G ru
%F MZM_2022_112_1_a1
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/

[1] O. Yu. Aristov, “Nekommutativnye funktsii klassa $C^\infty$ v kontekste treugolnykh algebr Li”, Izv. RAN. Ser. matem., 86:6 (2022) (to appear)

[2] A. A. Dosi, “Taylor functional calculus for supernilpotent Lie algebra of operators”, J. Operator Theory, 63:1 (2010), 191–216 | MR | Zbl

[3] A. A. Dosiev (Dosi), “Formally-radical functions in elements of a nilpotent Lie algebra and noncommutative localizations”, Algebra Colloq., 17, Special Issue no. 1 (2010), 749–788 | DOI | MR | Zbl

[4] A. Ya. Khelemskii, Banakhovy i polinormirovannye algebry: obschaya teoriya, predstavleniya, gomologii, Nauka, M., 1989 | MR

[5] O. Yu. Aristov, Obolochki v klasse banakhovykh algebr polinomialnogo rosta i $C^\infty$-funktsii ot svobodnykh peremennykh, Preprint, 2021

[6] W. Rudin, Real and Complex Analysis, McGraw-Hill Book, New York, 1987 | MR | Zbl