After loading the home page. ( don't use the mouse)
use the tab key to navigate to the "Create new group" button above the quick links.
If you press return you can get the "Create a new group" to "open".
However there is no way to select/activate the drop down menu to choose the other items:
Create new attribute definition
Create new attribute name
Create new folder
Create new Group
Add members to group

Maybe you can add a href="#" to the
body > div.top-container > div.container-fluid > div:nth-child(2) > div.span3.left-column > div.btn-group.btn-group-create.open > a.btn.btn-bigger.btn-create.dropdown-toggle tag
element?

That appears to make it keyboard accessible in chrome for me.