Integral calculus on quantum exterior algebras

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Serkan Karaçuha (Author) FCUP; Christian Lomp (Author) FCUP

Journal

Title: International Journal of Geometric Methods in Modern Physics

ISSN: 0219-8878

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-009-B4M

DOI: 10.1142/S0219887814500261

Abstract (EN): Hom-connections and associated integral forms have been introduced and studied by Brzezinski as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Omega, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzezinski et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom. 4 (2010) 281-312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

Language: English

Type (Professor's evaluation): Scientific