Gleason's problem associated to a real ternary algebra and applications
type: Item
instance of: scholarly article
title: Gleason's problem associated to a real ternary algebra and applications
zbMATH Open document ID: 1405.30049
author: Daniel Alpay
author: A. Vajiac
author: M. B. Vajiac
published in: Advances in Applied Clifford Algebras
publication date: 2018-08-15T00:00:00Z
review text: This paper deals with the study of a class of regular functions defined on a real ternary algebra. After a description and some remarks on ternary algebras, the authors highlight a special basis constructed upon a choice of idempotent elements. This leads them to define two differential operators akin to Cauchy-Riemann(-Fueter) ones. Afterwards, they study the theory of functions in the kernel of such operators, noticing some similarity with the Fueter theory in the quaternionic case. With the help of Fueter-like variables, they are able to state and prove a Gleason-like theorem. Then they recognize an analyticity behaviour of such regular functions, with respect to Fueter-like variables and, hence, give a characterization of regular rational functions of a Fueter-like variable. In the last part of the paper an application to Drury-Arveson spaces is announced.
reviewed by: Amedeo Altavilla
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 30A05
zbMATH DE Number: 6918627
zbMATH Keywords: ternary analysis
zbMATH Keywords: regular functions
zbMATH Keywords: Gleason's problem
zbMATH Keywords: Fueter variables
MaRDI profile type: Publication
full work available at URL: s00006-018-0857-8
OpenAlex ID: W2800799966
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DOI: 10.1007/S00006-018-0857-8
description: scientific article; zbMATH DE number 6918627