Journal of Lie Theory

no. 1
Atiyah Classes of Lie Bialgebras
Wei Hong1
1School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 263-275
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.
DOI: 10.5802/jolt.1058
Classification: 17B56, 17B62
Keywords: Atiyah class, Lie bialgebras, Lie algebra pair

Wei Hong  1

1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 
Wei Hong. Atiyah Classes of Lie Bialgebras. Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 263-275. doi: 10.5802/jolt.1058
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     author = {Wei Hong},
     title = {Atiyah {Classes} of {Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {263--275},
     year = {2019},
     volume = {29},
     number = {1},
     doi = {10.5802/jolt.1058},
     zbl = {1436.17027},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1058/}
}
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