How can X, Y, Z and W go above one in a quaternion animation on Blender? I am trying to import a collada file generated by Maya on Blender and that file was exported using what I think is the correct representation of a quaternion (x, y, z and w elements are between 0 and 1) and that file is not imported correctly by blender.

I am not an expert in mathematics but as far as I know, the elements x, y, z and w on quaternions are normalized, so they should never go above 1, they always vary between 0 and 1. So, Maya is correct.

When I create a quaternion animation on Blender, I see that Blender allows these elements to go above 1 and apparently the sky is the limit.

How can that be? Is there a way to make Blender work with quaternions between 0 and 1 and import that file correctly?
But....Blender does work with quaternions between 0 and 1. 

There's an interesting video put out by Nathan Vegdahl (that's part of his Humane Rigging series) that discusses quaternions: https://www.youtube.com/watch?v=FRD0PgsY3pU&amp;index=14&amp;list=PLE211C8C41F1AFBAB
If you go to about 10:31 in the video, it talks about quaternions only being valid between 0 and 1. By 11:09, he mentions what Blender does with values greater than 1. 

Not sure what would prevent the file from being imported correctly.