Jacques Van Wyk, University of Waterloo
Generalised Complex Structures on Products of Lie Groups
Let \(M\) be an even-dimensional manifold, and let \(H\) be a closed three-form on \(M\). An \(H\)-twisted generalised complex structure on \(M\) is an endomorphism of \(TM \oplus T^*M\) which squares to −1, preserves the natural pseudometric of \(TM \oplus T^*M\), and whose \(i\)-eigenbundle is closed under the \(H\)-twisted Dorfman bracket. A natural question is given a fixed closed three-form \(H\) on \(M\), does there exist an \(H\)-twisted generalised complex structure on \(M\)? We explore this question for products of compact simple Lie groups. This is motivated by Marco Gualtieri’s result that any even-dimensional Lie group with a biinvariant metric admits a generalised complex structure.
MC 4058