




Graded qDifferential Algebra Approach to ChernSimons Form 

PP: 2938 

Author(s) 

Viktor Abramov,
Olga Liivapuu,


Abstract 

In the present paper we develop noncommutative approach to a connection which is based on a notion of graded qdifferential
algebra, where q is a primitive Nth root of unity. We define the curvature of connection form and prove Bianchi identity.
We construct a graded qdifferential algebra to calculate the curvature of connection for any integer N 2. Making use of Bianchi
identity we introduce the Chern character form of connection form and show that this form is closed. We study the case N = 3 which
is the first nontrivial generalization because in the case N = 2 we have a classical theory. We calculate the curvature of connection
form and show that it can be expressed in terms of graded qcommutators, where q is a primitive cubic root of unity. This allows us to
prove an infinitesimal homotopy formula, and making use of this formula we introduce the ChernSimons form. 




