On quasi-number algebras
type: Item
instance of: scholarly article
title: On quasi-number algebras
zbMATH Open document ID: 0848.17044
DOI: 10.1016/0034-4877(92)90024-U
author: V. Pereyra
published in: Reports on Mathematical Physics
publication date: 1994-01-09T00:00:00Z
review text: Generalizations of complex numbers suggested by Weierstrass, Bruwier, Mikusinski and other are investigated in detail. These generalizations are related to hyperbolic and elliptic mappings via polar representation of the so-called quasinumbers proposed by Fleury and others. Relevance of these quasi-number systems to Potts-like models, fractals and Weyl's finite quantum mechanics with discrete configuration space is indicated. The note is based on the book ``On Hyperbolic and Elliptic Mappings and Quasi-number Algebras'' by the first author (Warsaw University Division Publication, A. Hecel and Z. Kulikowski, Polygraph, November 1991, Bialystock, Poland). The contents of the note are: Introduction, the notion of elliptic and hyperbolic quasi-numbers, matrix representation of elliptic and hyperbolic quasi-numbers, groups of nonzero-volume quasi-numbers, polarform of nonzero-volume quasi-numbers, finally remarks (relation with Potts-model and other historical remarks).
Mathematics Subject Classification ID: 17B81
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 81R99
zbMATH DE Number: 459131
reviewed by: Anna P. Helversen-Pasotto
MaRDI profile type: Publication
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full work available at URL: 0034-4877(92)90024-u
OpenAlex ID: W2135294868
description: scientific article; zbMATH DE number 459131