×

Survey of non-Desarguesian planes. (English) Zbl 1160.51001

This is a survey of the connections between projective planes and algebraic structures. In addition to the connection between projective planes and simple complemented modular lattices, one has the connections between projective planes and the algebraic structures their lines carry, which constitute the main object of interest of the author. In this way, one stumbles upon ternary rings, near-fields, quasi-fields, and alternative division rings, the algebraic counterparts of certain classes of projective planes in the Lenz-Barlotti classification. AndrĂ©’s classification of translation planes concludes the survey.

MSC:

51-02 Research exposition (monographs, survey articles) pertaining to geometry
51-03 History of geometry
51A35 Non-Desarguesian affine and projective planes
01A60 History of mathematics in the 20th century
PDFBibTeX XMLCite