# Graded derivations of the algebra of differential forms associated with a connection

@article{Michor1989GradedDO, title={Graded derivations of the algebra of differential forms associated with a connection}, author={Peter W. Michor}, journal={Lecture Notes in Mathematics}, year={1989}, volume={1410}, pages={249-261} }

The central part of calculus on manifolds is usually the calculus of differential forms and the best known operators are exterior derivative, Lie derivatives, pullback and insertion operators. Differential forms are a graded commutative algebra and one may ask for the space of graded derivations of it. It was described by Frolicher and Nijenhuis in [1], who found that any such derivation is the sum of a Lie derivation Θ(K) and an insertion operator i(L) for tangent bundle valued differential…

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## References

SHOWING 1-10 OF 21 REFERENCES

Gauge Theory for Diffeomorphism Groups

- Mathematics
- 1988

We consider fibre bundles without structure group and develop the theory of connections, curvature, parallel transport, (nonlinear) frame bundle, the gauge group and it’s action on the space of…

Theory of Vector-Valued Differential Forms: Part I. Derivations in the Graded Ring of Differential Forms

- Mathematics
- 1956

Integral curves of derivations., to appear

- J. Global Analysis and Geometry

Theory of vector valued di erential forms

- Part I, Indagationes Math
- 1956

Determination of all natural bilinear operators of the type of the Frr olicher- Nijenhuis bracket

- Suppl. Rendiconti Circolo Mat. Palermo, Series II No
- 1987

Determination of all natural bilinear operators of the type of the Fr olicher- Nijenhuis bracket., Suppl

- Rendiconti Circolo Mat. Palermo, Series II No
- 1987

Determination of all natural bilinear operators of the type of the Frölicher- Nijenhuis bracket

- Suppl. Rendiconti Circolo Mat. Palermo, Series II No
- 1987

Determination of all natural bilinear operators of the type of the Frölicher- Nijenhuis bracket., Suppl

- Rendiconti Circolo Mat. Palermo, Series II No
- 1987

Gauge theory for di eomorphism groups

- Proceedings of the Conference on Di eren- tial Geometric Methods in Theoretical Physics,
- 1987