Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2015
    • (edited May 28th 2015)

    I see that (from long, long time ago) one section of the entry graded vector space defines “pre-graded” to mean \mathbb{Z}-graded and “graded” to be \mathbb{N}-graded.

    I am not sure if that is a good terminology, mainly because it seems not to be common. I came here from the entry dg-Lie algebra, wondering what that entry might actually mean by a “pre-graded” Lie algebra. (I should have commented on this long ago, of course).

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 28th 2015

    Weird. I’ve never ever heard that terminology. Where does it come from?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 28th 2015

    Tim will know more, I suppose. (?) But I’d suggest that even if it comes from somewhere, we should deprecate it. And at dg-Lie algebra we should accordingly edit to make it clear that in general in fact dg-Lie algebras are \mathbb{Z}-graded.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeMay 28th 2015

    Those pages were initially my attempt to understand Daniel Tanré’s lecture notes. I struck with his terminology at the time. I now find it awkward! \mathbb{Z}-graded is much clearer.

  1. Is the formula (fg)(vw)=(1) |g||f|(f(v)g(w))(f\otimes g) (v\otimes w) = (-1)^{|g||f|}(f(v) \otimes g(w)) the intended one (last section on the tensor product)? For me the formula (fg)(vw)=(1) |g||v|(f(v)g(w))(f\otimes g) (v\otimes w) = (-1)^{|g||v|}(f(v) \otimes g(w)) is the standard one, and the associated category is not monoidal, but rather supermonoidal.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2023

    Thanks for the heads-up. This formula is from revision 9.

    I am not sure what the intention of this category of “pre-gvs” really is.