{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T23:08:58Z","timestamp":1772752138912,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Geom. Methods Mod. Phys."],"published-print":{"date-parts":[[2014,4]]},"abstract":"<jats:p>Hom-connections and associated integral forms have been introduced and studied by Brzezi\u0144ski as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (\u03a9, 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 Brzezi\u0144ski et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281\u2013312]). 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.<\/jats:p>","DOI":"10.1142\/s0219887814500261","type":"journal-article","created":{"date-parts":[[2013,12,13]],"date-time":"2013-12-13T09:18:37Z","timestamp":1386926317000},"page":"1450026","source":"Crossref","is-referenced-by-count":6,"title":["Integral calculus on quantum exterior algebras"],"prefix":"10.1142","volume":"11","author":[{"given":"Serkan","family":"Kara\u00e7uha","sequence":"first","affiliation":[{"name":"Department of Mathematics, FCUP, University of Porto, Rua Campo Alegre 687, 4169-007 Porto, Portugal"}]},{"given":"Christian","family":"Lomp","sequence":"additional","affiliation":[{"name":"Department of Mathematics, FCUP, University of Porto, Rua Campo Alegre 687, 4169-007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2014,4,16]]},"reference":[{"key":"rf1","first-page":"257","volume":"62","author":"Connes A.","journal-title":"Publ. Math. Inst. Hautes \u00c9tudes Sci."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498808002977"},{"key":"rf3","volume":"6","author":"Brzezi\u0144ski T.","journal-title":"SIGMA"},{"key":"rf4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.4171\/jncg\/56","volume":"4","author":"Brzezi\u0144ski T.","journal-title":"J. Noncommut. Geom."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-98-04210-5"},{"key":"rf6","unstructured":"U.\u00a0Kr\u00e4\u00e9hmer, New Techniques in Hopf Algebras and Graded Ring Theory (K. Vlaam. Acad. Belgie Wet. Kunsten (KVAB), Brussels, 2007)\u00a0pp. 117\u2013125."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195176848"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8205-7"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2010-10585-3"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/9789812790019_0002"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011458821831"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60896-4"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S0219887811005440"}],"container-title":["International Journal of Geometric Methods in Modern Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219887814500261","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T13:15:49Z","timestamp":1716297349000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219887814500261"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2014,4,16]]},"published-print":{"date-parts":[[2014,4]]}},"alternative-id":["10.1142\/S0219887814500261"],"URL":"https:\/\/doi.org\/10.1142\/s0219887814500261","relation":{},"ISSN":["0219-8878","1793-6977"],"issn-type":[{"value":"0219-8878","type":"print"},{"value":"1793-6977","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4]]}}}