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The algebra of differential forms on a full matric bialgebra

Published online by Cambridge University Press:  24 October 2008

A. Sudbery
A. Sudbery
Affiliation:
Department of Mathematics, University of York, York, YO1 5DD
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Abstract

We construct a non-commutative analogue of the algebra of differential forms on the space of endomorphisms of a vector space, given a non-commutative algebra of functions and differential forms on the vector space. The construction yields a differential bialgebra which is a skew product of an algebra of functions and an algebra of differential forms with constant coefficients. We give necessary and sufficient conditions for such an algebra to exist, show that it is uniquely determined by the differential algebra on the vector space, and show that it is a non-commutative superpolynomial algebra in the matrix elements and their differentials (i.e. that it has the same dimensions of homogeneous components as in the classical case).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 111 - 130
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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