Divergences on Projective Modules and NonCommutative Integrals
Abstract
A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented. This leads to a construction of a first order differential calculus on such a module which admits a homconnection or a divergence. Properties of integrals associated to this divergence are studied, in particular the formula of integration by parts is derived. Specific examples include inner calculi on a noncommutative algebra, the Berezin integral on the supercircle and integrals on Hopf algebras.
 Publication:

International Journal of Geometric Methods in Modern Physics
 Pub Date:
 2011
 DOI:
 10.1142/S0219887811005440
 arXiv:
 arXiv:1010.1470
 Bibcode:
 2011IJGMM..08..885B
 Keywords:

 Mathematics  Quantum Algebra;
 58B32;
 16W25
 EPrint:
 13 pages