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Zbl 0701.58004
Vanžurová, Alena
Double vector spaces. (English)
[J] Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 88, Math. 26, 9-25 (1987). ISSN 0231-9721

In differential geometry of higher order, one deals with some interesting algebraical structures possessing partial operations. Here we shall investigate the simplest of them - double vector spaces and their morphisms. The category ${\cal D}{\cal L}$ of double linear morphisms has been introduced by {\it J. Pradines} in C. R. Acad. Sci., Paris, Sér. A 278, 1523-1526 (1974; Zbl 0285.58002). Analogous investigations in double affine and affine-linear case have been studied by {\it I. Kolář} in Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys. 24, 883-887 (1976; Zbl 0354.58002). In this paper we shall show a slightly more general point of view. The category ${\cal D}{\cal L}$ will be described geometrically.

MSC 2000:: *58A20 Jets
58A30 Vector distributions (global analysis)
55R65 Generalizations of fiber spaces and bundles

Keywords: double vector spaces; morphisms; double linear morphisms

Citations: Zbl 0285.58002; Zbl 0354.58002

Cited in: Zbl 0762.53014

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