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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 7th 2012
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 7th 2012

    interesting description. I see that the entry symbol map treats something what can be interpreted as a very special case, namely of a Clifford algebra. On the other hand, when one has a filtered algebra whose associated graded is commutative, one can define a symbol map in much more generality, and the notion can be sheafified. The result is far more general than both notions (symbol map for Clifford algebras and symbol map for algebras and sheaves of differential operators) and widely used. Once I have a thought I will try to write something along those lines (or if somebody else is quicker than somebody else will).

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 14th 2022
    • (edited Aug 14th 2022)
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 14th 2022
    • (edited Aug 14th 2022)

    Thanks for the alert. I have added (here) the missing symbol “T *T^\ast” and an explicit link to p. 13 in the referenced note, which is all that this sentence is pointing out.

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeSep 12th 2023

    I removed redirect to principal symbol in the wake of creating a separate entry. Separating has several reasons, first of all it is not the same, and second, principal symbol is usually defined in the more general context of pseudodifferential operators; there are also versions in some filtered ring-theoretic setups.

    diff, v9, current