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Journal of Lie Theory 29 (2019), No. 1, 263--275
Copyright Heldermann Verlag 2019

Atiyah Classes of Lie Bialgebras

Wei Hong
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

The Atiyah class was originally introduced by M. F. Atiyah. It has many developments in recent years. One important case is the Atiyah classes of Lie algebra pairs. In this paper, we study the Atiyah class of the Lie algebra pair associated with a Lie bialgebra (g, g*). A simple description of the Atiyah class and the first scalar Atiyah class is given by the Lie algebra structures on g and g*. As an application, the Atiyah classes for some special cases are investigated.

Keywords: Atiyah class, Lie bialgebras, Lie algebra pair.

MSC: 17B56, 17B62

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