I heard from some people working in Lie super algebra that there was no proper definition for Weyl group of Lie super algebra. I do not know Lie super algebra at all. But When I searched on Google, I found that it seems there still exists some definitions of Weyl group.

I wonder whether there is a well-accepted definition for it.

The reason I want to ask this question is that I need Weyl group for Lie super algebra to play with the geometry related to super Lie algebra.

Another question is that I heard from some experts in Lie super algebra that there was no well-accepted super geometry related to Lie super algebra.

However, It seems that one of the students of Manin, who is Dimitry Leites ever developed supergeometry.