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nLab > Latest Changes: pin group

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2019

    added a line on Pin ±(n)Pin_\pm(n), and added pointer to the example of Pin(2)

    diff, v5, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 2nd 2019
    • (edited Apr 2nd 2019)

    The article pin group says

    The Pin group Pin(V;q) of a quadratic vector space, def. 2.1, is the subgroup of the group of units in the Clifford algebra Cl(V,q) Pin(V,q)↪GL 1(Cl(V,q)) on those elements which are multiples v_1 \cdots v_{2k} of elements v_i \in V with q(V) = 1.

    It appears that this defines the spin group, not the pin group, because 2k is even. For the pin group one needs to allow an arbitrary number of v_i.

    The same problem seems to be present in the article spin group.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 2nd 2019

    Thanks for catching. Fixed now (both entries). Also fixed the typo right afterwards, (capital VV to lower case).

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 17th 2019

    Added Pin(5) to the examples.

    diff, v8, current

  5. In dimension 2 exists no universal covering for O(2), so we have to restricts to double covering of O(2), similar to the spin(2) case.

    Julian Seipel

    diff, v11, current

1 to 5 of 5

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