Coisotropic Subalgebras of Complex Semisimple Lie Bialgebras

Doctoral Dissertation
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Abstract

Given a complex, semisimple Lie biaglebra, we consider the coisotropic subalgebras–the Lie subalgebras of whose annihilator in the dual space is a Lie subalgebra of the dual space. M. Zambon gives a construction for certain coisotropic sugalgebras, he explains his construction explicitly for the classical simple Lie algebras. In this dissertation, we explicitly compute Zambon’s coisotroic subalgebras for a general complex semisimple Lie algebra and show that these coisotropic subalgebaras are a special case of a more general construction.
Furthermore, we view coisotropic subalgebras of inside the variety of Lagrangian subalgebras of the double.

Attributes

Attribute NameValues
URN
  • etd-06192014-135309

Author Nicole Rae Kroeger
Advisor Sam Evens
Contributor Brian Hall, Committee Member
Contributor Sam Evens, Committee Chair
Contributor Michael Gekhtman, Committee Member
Contributor Matthew Dyer, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2014-05-16

Submission Date 2014-06-19
Country
  • United States of America

Subject
  • coisotropic subalgebras

  • Lie algebras

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units

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