∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
A double Lie algebroid is the Lie algebroid-analog of a Lie groupoid-double groupoid; essentially a Lie algebroid object internal to the category of Lie algebroids.
For a Lie algebroid, its tangent double Lie algebroid is the degreewise tangent Lie algebroid of the base space and of the total space , respectively
For
a double Lie groupoid, applying Lie differentiation degreewise yields a double Lie algebroid
The notion originates somewhere around
Further discussion is in
Kirill Mackenzie, Double Lie algebroids and second-order geometry. I. Adv. Math. 94 (1992), no. 2, 180–239
Double Lie algebroids and second-order geometry. II. Adv.Math. 154 (2000), no. 1, 46–75. dg-ga/9712013).
A textbook account is in
Last revised on March 25, 2013 at 22:17:10. See the history of this page for a list of all contributions to it.