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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2017
    • (edited Dec 17th 2017)

    For (V ,d)(V^\bullet,d) a cochain complex in characteristic zero, the cohomology of its graded symmetric dg-algebra should be the graded symmetric algebra on its cohomology

    H (Sym(V ,d))Sym(H (V,d)). H^\bullet(Sym(V^\bullet,d)) \;\simeq\; Sym( H^\bullet(V,d) ) \,.

    (now recorded at symmetric algebra: here)

    I just want to cite this from the literature. This must be a textbook fact (in char = 0 at least); but the only reference I find is this MO discussion here.

    Anyone has a more canonical citation (for char = 0) at your fingertips?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2017
    • (edited Dec 17th 2017)

    I have spelled out the proof that for finite groups in char = 0 (at least) taking invariants commutes with taking cochain cohomology: here. And made this a proof of the above fact: there