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The algebra of differential forms on a full matric bialgebra. (English) Zbl 0791.17016

If \(M\) is a bialgebra over a field \(k\), \(M\) is called a matric bialgebra if it is generated by \(x_{ij}\), \(i,j=1,\dots,n\), such that \(\Delta (x_{ij})=\sum^ n_{t=1} x_{it} \otimes x_{tj}\), \(\varepsilon (x_{ij})=\delta_{ij}\). A full matric bialgebra is one whose algebra is a polynomial algebra. The author gives a construction of an algebra of differential forms for any full matric bialgebra determined by a differential algebra on a vector space. He then shows that this algebra is uniquely determined by certain natural properties and that it is a flat deformation of the classical algebra of polynomial differential forms.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
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References:

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