Year: 1992
Type: preprint
Abstract: Let $G\subset GL(V)$ be a linear Lie group with Lie algebra $\frak g$ and let $A(\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative supercommutative algebra $A(\frak g)= S(\frak g^*)\otimes \La(V^*)$. To any $G$-structure $π:P\to M$ with a connection $ω$ we associate a homomorphism $μ_ω:A(\frak g)^G\to Ω(M)$. The differential forms $μ_ω(f)$ for $f\in A(\frak g)^G$ which are associated to the $G$-structure $π$ can be used to construct Lagrangians. If $ω$ has no torsion the differential forms $μ_ω(f)$ are closed and define characteristic classes of a $G$-structure. The induced homomorphism $μ'_ω:A(\g)^G\to H^*(M)$ does not depend on the choice of the torsionfree connection $ω$ and it is the natural generalization of the Chern Weil homomorphism.
Source: arXiv (Cornell University)
Authors: Alekseevsky, Dimitri, Michor, Peter W.
Institution: University of Vienna
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W2951765889