\(N\)-complex, graded \(q\)-differential algebra and \(N\)-connection on modules. (English) Zbl 1371.16010

Abramov, Viktor; Liivapuu, Olga

J. Gen. Lie Theory Appl. 9, No. S1, Article ID 006, 11 p. (2015).

Summary: It is well known that given a differential module \(E\) with a differential \(d\) we can measure the non-exactness of this differential module by its homologies which are based on the key relation \(d^2=0\). This relation is a basis for several important structures in modern mathematics and theoretical physics to point out only two of them which are the theory of de Rham cohomologies on smooth manifolds and the apparatus of BRST-quantization in gauge field theories.

MSC:

16E45	Differential graded algebras and applications (associative algebraic aspects)
58A12	de Rham theory in global analysis

Keywords:

\(N\)-differential module; cohomologies of \(N\)-cochain complex; graded \(q\)-differential algebra; algebra of connection form; \(N\)-connection form; covariant \(N\)-differential; \(N\)-cochain complex; \(N\)-curvature form; \(N\)-connection on module; curvature of \(N\)-connection; \(N\)-connection consistent with Hermitian structure of module