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Coisotropic subalgebras of complex semisimple Lie bialgebras


Author: Nicole Kroeger
Journal: Proc. Amer. Math. Soc. 144 (2016), 473-486
MSC (2010): Primary 17B62; Secondary 53D17
DOI: https://doi.org/10.1090/proc12710
Published electronically: June 9, 2015
MathSciNet review: 3430827
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Abstract: In his paper ``A Construction for Coisotropic Subalgebras of Lie Bialgebras'', Marco Zambon gave a way to use a long root of a complex semisimple Lie bialgebra $ \mathfrak{g}$ to construct a coisotropic subalgebra of $ \mathfrak{g}$. In this paper, we generalize Zambon's construction. Our construction is based on the theory of Lagrangian subalgebras of the double $ \mathfrak{g}\oplus \mathfrak{g}$ of $ \mathfrak{g}$, and our coisotropic subalgebras correspond to torus fixed points in the variety $ \mathcal {L}(\mathfrak{g}\oplus \mathfrak{g})$ of Lagrangian subalgebras of $ \mathfrak{g}\oplus \mathfrak{g}$.


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Additional Information

Nicole Kroeger
Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, Indiana 46556
Address at time of publication: South Carolina Governor’s School for Science and Mathematics, 401 Railroad Avenue, Hartsville, South Carolina 29550
Email: nkroeger@alumni.nd.edu

DOI: https://doi.org/10.1090/proc12710
Received by editor(s): September 8, 2014
Received by editor(s) in revised form: January 1, 2015
Published electronically: June 9, 2015
Additional Notes: The author was supported in part by the Arthur J. Schmitt Foundation.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society