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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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


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:
  • 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:
  • MathSciNet review: 3430827