On quasi-number algebras
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).
scientific article; zbMATH DE number 459131