# Differential calculus on almost commutative algebras and applications to the quantum hyperplane

Archivum Mathematicum (2005)

- Volume: 041, Issue: 4, page 359-377
- ISSN: 0044-8753

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topCiupală, Cătălin. "Differential calculus on almost commutative algebras and applications to the quantum hyperplane." Archivum Mathematicum 041.4 (2005): 359-377. <http://eudml.org/doc/249479>.

@article{Ciupală2005,

abstract = {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.},

author = {Ciupală, Cătălin},

journal = {Archivum Mathematicum},

keywords = {noncommutative geometry; almost commutative algebra; linear connections; quantum hyperplane; noncommutative geometry},

language = {eng},

number = {4},

pages = {359-377},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Differential calculus on almost commutative algebras and applications to the quantum hyperplane},

url = {http://eudml.org/doc/249479},

volume = {041},

year = {2005},

}

TY - JOUR

AU - Ciupală, Cătălin

TI - Differential calculus on almost commutative algebras and applications to the quantum hyperplane

JO - Archivum Mathematicum

PY - 2005

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 041

IS - 4

SP - 359

EP - 377

AB - 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.

LA - eng

KW - noncommutative geometry; almost commutative algebra; linear connections; quantum hyperplane; noncommutative geometry

UR - http://eudml.org/doc/249479

ER -

## References

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