Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Kirill Mackenzie
Affiliation:

Sheffield
Date:

Wed, 2018-12-05 10:30 - 12:00 For any vector bundle $A$ there is a canonical diffeomorphism $R: T^*(A^*)\to T^*(A)$ introduced by

Ping Xu and the speaker (Duke Math. J. 1994). We describe this in detail and show how it can be extended

to the duals of any double vector bundle. This leads in a natural way to the concept of double Lie algebroid

(Crelle, 2011). We show that the double Lie algebroid structure on the cotangent double of a Lie bialgebroid

is a natural abstraction of the structure of a Poisson Lie group(oid) and we briefly consider other important

instances of double Lie algebroids and alternative approaches.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/3946