Zoran Skoda noncommutative Chern-Weil theory

There are various analogues of Chern-Weil theory, Weil algebra and Chern-Weil homomorphism in noncommutative geometry.

• A. Alekseev, E. Meinrenken, The non-commutative Weil algebra, Invent. Math. 139, n. 1, 135–172, 2000, doi

• A. Alekseev, E. Meinrenken, Lie theory and the Chern-Weil homomorphism, Ann. Scient. Éc. Norm. Sup., 4e série, 38 (2005) 303–338 pdf

• P. M. Hajac, T. Maszczyk, Cyclic-homology Chern–Weil theory for families of principal coactions, Commun. Math. Phys. 381, 707–734 (2021) doi

• Marius Crainic, Cyclic cohomology of Hopf algebras, Journal of Pure and Applied Algebra 166:1–2 (2002) 29–66 doi

• M. Dubois-Violette, G. Landi, The Weil algebra of a Hopf algebra I: A noncommutative framework, Commun. Math. Phys. 326, 851–874 (2014) doi

It is useful also to compare to algebraic models in usual and formal geometry

• I. M. Gelfand, M. M. Smirnov, (1996) Chern-Simons classes and cocycles on the Lie algebra of the gauge group, In: Gelfand, I.M., Lepowsky, J., Smirnov, M.M. (eds) The Gelfand Mathematical Seminars, 1993–1995. Birkhäuser Boston doi