Biharmonic bases in algebras of the second rank
type: Item
instance of: scholarly article
title: Biharmonic bases in algebras of the second rank
zbMATH Open document ID: 0619.30049
DOI: 10.1007/BF01058492
author: I. P. Mel'nichenko
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let A be an algebra over \({\mathbb{C}}\) of dimension 2, a basis of A, \(\{e_ 1,e_ 2\}\), with nilpotent \(e^ 2_ 1+e^ 2_ 2\neq 0\) is called biharmonic, as the components of Hausdorff differentiable functions from A to A are biharmonic, see the author and \textit{V. F. Kovalev} [Dokl. Akad. Nauk Ukr. SSR, Ser. A. 1981, No.8, 26-27 (1981; Zbl 0472.31001)]. In this paper the algebras are determined which have at least one biharmonic basis, the possible forms of such a basis are discussed.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 16N40
zbMATH DE Number: 4004586
zbMATH Keywords: differentiable functions in algebra
zbMATH Keywords: Hausdorff differentiable
zbMATH Keywords: biharmonic basis
reviewed by: Klaus Habetha
MaRDI profile type: Publication
cites work: Q3337726
cites work: Q5801454
full work available at URL: https://doi.org/10.1007/bf01058492
OpenAlex ID: W2045967400
description: scientific article; zbMATH DE number 4004586