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nLab > Latest Changes: Clifford algebra

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 27th 2017
    • (edited Jan 27th 2017)

    The entry Clifford algebra used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:

    Just the bare statements so far.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2020
    • (edited Apr 26th 2020)

    added some more publication data to the references, added pointer to one more brief introduction, and reorganized the items slightly

    diff, v23, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2020

    added (here) the statement and its proof (i.e. the elementary computation) of the Clifford representation of the orthognal Lie algebras

    diff, v25, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2021
    • (edited Sep 4th 2021)

    have added these two pointers:

    Will also add these to standard model of particle physics.

    diff, v27, current

  5. In quaternions i, j, and k square to -1. Therefore it should be Cl 3,0≃ℍCl_{3,0} \simeq \mathbb{H}, instead of Cl 2,0≃ℍCl_{2,0} \simeq \mathbb{H}, right?

    Anonymous

    diff, v29, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 26th 2022
    • (edited Oct 26th 2022)

    Isn’t it that from the two basis elements of ℝ (2,0)\mathbb{R}^{(2,0)}, e 1e_1 and e 2e_2 squaring to −1-1, the Clifford algebra is generated by {1,e 1,e 2,e 1e 2}\{1, e_1, e_2, e_1 e_2\}, the latter three generators squaring to −1-1?

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2022

    Yes. Ideally the entry would explain how the identification works. (Myself, i have no time right now, maybe later…)

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 26th 2022

    I’ve rolled back to version #28.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 26th 2022

    Added a small clarification regarding #6.

    diff, v31, current

  10. Added a small clarification regarding #6.

    Aurelius

    diff, v32, current

  11. Added algebra - contents to sidebar

    Anonymouse

    diff, v36, current

1 to 11 of 11

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