Liana David
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We define the notions of $B_n$ generalized pseudo-Hermitian and $B_n$ generalized pseudo-Kähler structures on an odd exact Courant algebroid $E$. When $E$ is in the standard form (or of type $B_n$) we express these notions in terms of classical tensor fields on the base of $E$. This is analogous to the bi-Hermitian viewpoint on generalized Kähler structures on exact Courant algebroids. We describe left-invariant $B_n$ generalized pseudo-Lähler structures on Courant algebroids of type $B_n$ over Lie groups of dimension two, three and four. This is joint work with Vicente Cortes (accepted in J. Geom Analysis 2023)