Journal of Generalized Lie Theory and Applications

On jets, extensions and characteristic classes I


Full-text: Open access


In this paper, we give general definitions of non-commutative jets in the local and global situation using square zero extensions and derivations. We study the functors $\operatorname{Exan}_k(A,I)$, where $A$ is any $k$-algebra, and $I$ is any left and right $A$-module and use this to construct affine non-commutative jets. We also study the Kodaira-Spencer class $\operatorname{KS}(\mathcal{L})$ and relate it to the Atiyah class.

Article information

J. Gen. Lie Theory Appl., Volume 4 (2010), Article ID G091101, 17 pages.

First available in Project Euclid: 11 October 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]


MAAKESTAD, Helge. On jets, extensions and characteristic classes I. J. Gen. Lie Theory Appl. 4 (2010), Article ID G091101, 17 pages. doi:10.4303/jglta/G091101.

Export citation


  • M. André. Homologie des algèbres commutatives. Die Grundlehren der mathematischen Wissenschaften, 206, Springer-Verlag, Berlin, 1974.
  • M. Atiyah. Complex analytic connections in fibre bundles. Trans. Amer. Math. Soc., 85 (1957), 181–207.
  • A. Grothendieck. Éléments de géométrie algébrique. IV. Étude locale de schémas et des morphismes de schémas. Inst. Hautes Études Sci. Publ. Math., 20 (1964), 101–355.
  • M. Karoubi. Homologie cyclique et $K$-theorie. Astérisque, no. 149 (1987), 147.
  • H. Maakestad. A note on principal parts on projective space and linear representations. Proc. Amer. Math. Soc., 133 (2005), 349–355.
  • H. Maakestad. Chern classes and Lie-Rinehart algebras. Indag. Math. (N.S.), 18 (2007), 589–599.
  • H. Maakestad. Chern classes and $\Exan$ functors. Preprint 2009.
  • H. Maakestad. Principal parts on the projective line over arbitrary rings. Manuscripta Math., 126 (2008), 443–464.