On this page:
1 Canonical odd vector field
1.1 General definition of -parameter families of diffeomorphisms
1.2 Case of odd tangent bundle
2 Odd tangent bundle of a group

Properties of odd tangent bundle

1 Canonical odd vector field

1.1 General definition of -parameter families of diffeomorphisms

In the language of functors of points, a -parameter group of diffeomorphisms of a supermanifold is defined as a map, for any supermanifold :

consistent with morphisms between different ’s.

1.2 Case of odd tangent bundle

For any supermanifold , the has a canonically defined -parameter group of diffeomorphisms. It is defined as follows. For any define a “shift”:

    

  

Then define the map:

2 Odd tangent bundle of a group

If is a supergroup, then is again a supergroup.