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nLab > Latest Changes: decomposable differential form

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 23rd 2018
    • (edited Feb 23rd 2018)

    For purposes of linking, I had given an entry to decomposable differential form.

    In more general ℕ\mathbb{N}-graded-commutative algebras than just that of differential forms, is there any established terminology for

    0.\;\;\;\;\;0. elements that are sums of decomposables, i.e. sums of monomials in elements of degree 1?

    What I’d really need is terminology for:

    1. elements HH of degree n+1n+1 which split off at least one factor of degree 11, hence H=α⏟deg=1⋅βH = \underset{deg = 1}{\underbrace{ \alpha}} \cdot \beta;

    2. elements which are finite sums of these.

    Is there anything?

  2. For 2. you could call it the ideal generate by elements of degree 1.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 23rd 2018
    • (edited Feb 24th 2018)

    True. But I am hoping for something more catchy that still has some “decompos-” in it.

    In parts of the physics literature they say “composite” and “decomposed” etc. for the 0th case, for instance here. This is convenient and suggestive, but unfortunately it is in conflict with the established convention in mathematics. I was hoping that with some qualifiers added in this could be disentangled.

    Does anyone say “weakly decomposable”? Or “sum-decomposable”? Or “quasi-decomposable”? Or something like this?

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