Holomorphy over Finite-dimensional Commutative Associative C-algebras: Local Theory

Authors

  • Marin Genov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

DOI:

https://doi.org/10.7546/CRABS.2024.05.02

Keywords:

analysis over commutative algebras, monogenic functions, hypercomplex analysis

Abstract

To a morphism $$\mathcal{A} \xrightarrow{\varphi} \mathcal{B}$$ of finite-dimensional commutative associative unital Banach $$\mathbb{C}$$-algebras one can associate a sheaf $$\mathcal{O}_\varphi$$ on the underlying topological space $$|\mathcal{A}|$$ of $$\mathcal{A}$$ consisting of $$\mathcal{B}$$-valued differentiable functions $$f$$ with $$\mathcal{A}$$-linear differential $$Df$$. It turns out that this class of functions exhibits a theory very similar to the classical complex analysis of one variable. In this article we give only an overview of some new results concerning the fundamentals of the corresponding local theory while at the same time also strengthen various already existing results scattered throughout the literature.

Author Biography

Marin Genov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mailing Address:
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8,
1113 Sofia, Bulgaria

E-mail: marin.genov@math.bas.bg

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Published

25-05-2024

How to Cite

[1]
M. Genov, “Holomorphy over Finite-dimensional Commutative Associative C-algebras: Local Theory”, C. R. Acad. Bulg. Sci. , vol. 77, no. 5, pp. 646–656, May 2024.

Issue

Section

Mathematics