On the variety of Lagrangian subalgebras, II

By S. Evens, Jiang-Hua Lu. 2001

77 citations recorded by the source corpus.

We study Lagrangian subalgebras of a semisimple Lie algebra with respect to the imaginary part of the Killing form. We show that the variety L of Lagrangian subalgebras carries a natural Poisson structure �. We determine the irreducible components of L, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the real points of a De Concini-Procesi compactification and a compact homogeneous ′

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b4199dcb39178826509f5df3b6d5f85ee180d171

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. E. Meinrenken
2. David Li-Bland
3. R. Pink
4. T. Wedhorn
5. Jonathan Pila
6. R. Mehta
7. Ehud Hrushovski
8. R. Rocha

In Geometry and Topology

1. Paul Ziegler
2. R. Pink
3. E. Meinrenken
4. David Li-Bland
5. T. Wedhorn
6. Chao Zhang
7. Jonathan Pila
8. Xuhua He

In Mathematical Physics

1. Paul Ziegler
2. R. Pink
3. E. Meinrenken
4. David Li-Bland
5. T. Wedhorn
6. Chao Zhang
7. Christopher J. Schommer-Pries
8. Xuhua He

Citations in the corpus

• Algebraic zip data (2010, background): “atics, University of Paderborn, D-33098 Paderborn, Germany, wedhorn@math.uni-paderborn.de ‡Dept. ofMathematics,ETHZu¨richCH-8092Zu¨rich,Switzerland,paul.ziegler@math.ethz.ch 1 proved by Evens and Lu ([EL]), that for certain Poisson structure, each G-orbit on ZI is a Poisson submanifold. In [MW] Moon”
• Courant Algebroids and Poisson Geometry (2008, methodology): “× d is a Courant algebroid. A similar argument applies more generally to the variety of co-isotropic subalgebras of any given dimension. These examples are related: For instance, as shown by Evens-Lu [12] the de ConciniProcesi compactification of Gis one of the irreducible components of the variety o”