Differential calculus on almost commutative algebras and applications to the quantum hyperplane
Ciupală, Cătălin
Archivum Mathematicum, Tome 041 (2005), p. 359-377 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2005-01-01
Classification:  16E45,  16W35,  16W50,  58C50,  81R60 
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     author = {C\u at\u alin Ciupal\u a},
     title = {Differential calculus on almost commutative algebras and applications to the quantum hyperplane},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {359-377},
     zbl = {1110.81111},
     mrnumber = {2195490},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107966}
}

Ciupală, Cătălin. Differential calculus on almost commutative algebras and applications to the quantum hyperplane. Archivum Mathematicum, Tome 041 (2005) pp. 359-377. http://gdmltest.u-ga.fr/item/107966/

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