On local linear convexity generalized to commutative algebras
Complex Variables
2020-09-29 v1
Abstract
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there is at least one that is non-degenerate. The notion of linearly convex domains in the multi-dimensional complex space and some of their properties are generalized to the space that is the Cartesian product of n algebras A. Namely, the separate necessary and sufficient conditions of the local A-linear convexity of domains with smooth boundary in the space are obtained in terms of nonnegativity and positivity of formal quadratic differential form in A, respectively.
Cite
@article{arxiv.2009.13306,
title = {On local linear convexity generalized to commutative algebras},
author = {T. M. Osipchuk},
journal= {arXiv preprint arXiv:2009.13306},
year = {2020}
}