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nLab > Latest Changes: Grassmann algebra vs exterior algebra

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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeOct 24th 2009

    John put in a definition at Grassmann algebra. Should these be distinguished from exterior algebra?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 24th 2009

    I merged the two entries. I decided to make "Grassmann algebra" an example at exterior algebra taking the point of view that Grassmann algebra is specifically the exterior algebra over a (graded) vector space.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeOct 24th 2009
    I agree that Grassmann algebra is the exterior algebra ON the vector space, and this terminology is used more in physics. Exterior algebra is more generally used term and it is on a module. I slightly prefer "on" rather than over, because over pertains to the ground commutative ring which is also involved here.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 24th 2009
    • (edited Oct 24th 2009)

    right, I should have said on. In particular since there is the important class of examples of exterior algebras ON modules OVER rings, such as notably the deRham complex.

1 to 4 of 4

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