| Title:
|
A generalization of the exterior product of differential forms combining Hom-valued forms (English) |
| Author:
|
Gross, Christian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
587-602 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This article deals with vector valued differential forms on $C^\infty$-manifolds. As a generalization of the exterior product, we introduce an operator that combines $\operatorname{Hom}(\bigotimes^s(W),Z)$-valued forms with $\operatorname{Hom}(\bigotimes^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles. (English) |
| Keyword:
|
differential forms |
| Keyword:
|
exterior product |
| Keyword:
|
multilinear algebra |
| MSC:
|
15A75 |
| MSC:
|
22E30 |
| MSC:
|
53C05 |
| MSC:
|
58A05 |
| MSC:
|
58A10 |
| MSC:
|
58A15 |
| idZBL:
|
Zbl 0946.58002 |
| idMR:
|
MR1485080 |
| . |
| Date available:
|
2009-01-08T18:36:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118957 |
| . |
| Reference:
|
[1] Greub W., Halperin S., Vanstone R.: Connections, Curvature, and Cohomology.Vol. II, Academic Press, 1973. Zbl 0372.57001 |
| Reference:
|
[2] Gross C.: Operators on differential forms for Lie transformation groups.Journal of Lie Theory 6 (1996), 1-17. Zbl 0872.58001, MR 1406002 |
| Reference:
|
[3] Gross C.: Connections on fiber bundles and canonical extensions of differential forms.http://www.mathematik.th-darmstadt.de/prepr, Preprint No. 1795. |
| Reference:
|
[4] Gross C.: Cohomology and connections on fiber bundles and applications to field theories.Journal of Mathematical Physics 37 12 (1996), 6375-6394. Zbl 0863.53017, MR 1419176 |
| Reference:
|
[5] Helgason S.: Differential Geometry and Symmetric Spaces.Academic Press, 1962. Zbl 0122.39901, MR 0145455 |
| Reference:
|
[6] Kobayashi S., Nomizu K.: Foundations of Differential Geometry.Vol. I, John Wiley & Sons, 1963. Zbl 0526.53001, MR 1393940 |
| . |
