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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Coisotropic subalgebras of complex semisimple Lie bialgebras
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by Nicole Kroeger PDF
Proc. Amer. Math. Soc. 144 (2016), 473-486 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 473-486
  • MSC (2010): Primary 17B62; Secondary 53D17
  • DOI: https://doi.org/10.1090/proc12710
  • MathSciNet review: 3430827