| Title:
|
Soldered double linear morphisms (English) |
| Author:
|
Vanžurová, Alena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
68-78 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Our aim is to show a method of finding all natural transformations of a functor $TT^*$ into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps $f:C_0\rightarrow C_0$ commuting with $TT^*$-soldered automorphisms of a double vector space $C_0=V^*\times V\times V^*$ are investigated. On the set $Z_s(C_0)$ of such mappings, appropriate partial operations are introduced. The natural transformations $TT^*\rightarrow TT^*$ are bijectively related with the elements of $Z_s((TT^*)_0\bold R^n)$. (English) |
| Keyword:
|
tangent functor |
| Keyword:
|
natural transformations |
| Keyword:
|
fibrations |
| Keyword:
|
double vector space |
| Keyword:
|
double vector fibration |
| Keyword:
|
soldering |
| MSC:
|
53C05 |
| MSC:
|
55R05 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0763.53032 |
| idMR:
|
MR1154056 |
| DOI:
|
10.21136/MB.1992.126230 |
| . |
| Date available:
|
2009-09-24T20:50:05Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126230 |
| . |
| Reference:
|
[1] I. Kolář: On jet prolongations of smooth categories.Bull. Acad. Polon. Sci., Math., astr. et phys. Vol. XXIV 10 (1976), 883-887. MR 0436190 |
| Reference:
|
[2] I. Kolář, Z.Radzisewski: Natural transformations of second tangent and cotangent functors.Czech. Math. Journal 38 (113) (1988), 274-279, Praha. MR 0946296 |
| Reference:
|
[3] J. Pradines: Représentation des jets non holonomes par des morphismes vectoriels doubles soudés.C.R.Acad. Sci Paris Sér. A 278 (1974), 1523-1527. Zbl 0285.58002, MR 0388432 |
| Reference:
|
[4] A. Vanžurová: Double vector spaces.Acta Univ. Palac. Olom., Fac. Rer. Nat., Math. XXVI 88 (1987), 9-25. MR 1033327 |
| Reference:
|
[5] A. Vanžurová: Double linear connections.AUPO (in press). |
| Reference:
|
[6] A. Vanžurová: Natural transformations of the second tangent functor and soldered morphisms.AUPO, to appear in 1992. MR 1212610 |
| . |
