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The Role of the Canonical Element in the Quantized Algebra of Differential Operators $\A\rtimes\U$

Chryssomalis Chryssomalakos·Peter Schupp·Paul Watts
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Abstract

We review the construction of the cross product algebra $\A\rtimes\U$ from two dually paired Hopf algebras $\U$ and $\A$. The canonical element in $\U \otimes \A$ is then introduced, and its properties examined. We find that it is useful for giving coactions on $\A\rtimes\U$, and it allows the construction of objects with specific invariance properties under these coactions. A ``vacuum operator'' is found which projects elements of $\A\rtimes\U$ onto said objects. We then discuss bicovariant vector fields in the context of the canonical element.

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Chryssomalis Chryssomalakos, Peter Schupp, Paul Watts. 1993-10-15. The Role of the Canonical Element in the Quantized Algebra of Differential Operators $\A\rtimes\U$. https://arxiv.org/abs/hep-th/9310100

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