What is a graded manifold?

There are several variations on the definition of “graded manifold”, and it can be a bit confusing for a newcomer. The goal of this post is to describe one definition that rules them all. This definition hopefully sheds some light on the relationships between the various types of graded manifolds.

I thought I had seen the definition in Kostant’s early treatise “Graded manifolds, graded Lie theory, and prequantization,” but, looking back at the paper now, I can’t find the definition there. In any case, I don’t claim any originality here. If anyone can remind me of the correct reference, I would appreciate it.

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First post, Emmy Noether

I’ve been debating for some time what to write about in my first post. As luck would have it, I discovered this recent New York Times article about Emmy Noether. Not that discovering the article was hard; it’s currently first on the list of “most emailed” articles.

I’m completely in agreement with Ransom Stephens, who said, “You can make a strong case that her theorem is the backbone on which all of modern physics is built.” Noether’s Theorem really does provide the organizing principle that underlies the Standard Model of particle physics.

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