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Title: Differential calculus on almost commutative algebras and applications to the quantum hyperplane (English)
Author: Ciupală, Cătălin
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 41
Issue: 4
Year: 2005
Pages: 359-377
Summary lang: English
Category: math
Summary: In this paper we introduce a new class of differential graded algebras named DG $\rho $-algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a $\rho $-algebra. Then we introduce linear connections on a $\rho $-bimodule $M$ over a $\rho $-algebra $A$ and extend these connections to the space of forms from $A$ to $M$. We apply these notions to the quantum hyperplane. (English)
Keyword: noncommutative geometry
Keyword: almost commutative algebra
Keyword: linear connections
Keyword: quantum hyperplane
MSC: 16E45
MSC: 16W35
MSC: 16W50
MSC: 58C50
MSC: 81R60
idZBL: Zbl 1110.81111
idMR: MR2195490
Date available: 2008-06-06T22:46:34Z
Last updated: 2012-05-10
Stable URL:
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