Abstract
In a seminal paper, Drinfel’d explained how to associate with every classical r-matrix, which are called triangular r-matrices by some authors, for a Lie algebra \( \mathfrak {g}\) a twisting element based on \({\mathcal {U}}(\mathfrak {g})[[\hbar ]]\), or equivalently a left invariant star product quantizing the left-invariant Poisson structure corresponding to r on the 1-connected Lie group G of \(\mathfrak {g}\) . In a recent paper, the authors solve the same problem by means of Fedosov quantization. In this short note, we provide a connection between the two constructions by computing the characteristic (Fedosov) class of the twist constructed by Drinfel’d and proving that it is the trivial class given by \( \frac{[\omega ]}{\hbar }\).
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Acknowledgements
The author is grateful to Chiara Esposito and Francesco D’Andrea for their encouragement to write this note. Special thanks go to the anonymous referee who gave valuable comments on the first version of this paper.
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Schnitzer, J. Characteristic (Fedosov-)class of a twist constructed by Drinfel’d. Lett Math Phys 110, 2353–2361 (2020). https://doi.org/10.1007/s11005-020-01291-z
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DOI: https://doi.org/10.1007/s11005-020-01291-z