Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: Clifford algebra

Bottom of Page

1 to 12 of 12

  1.  
    • 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 Cl3,0≃ℍ, instead of Cl2,0≃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), e1 and e2 squaring to −1, the Clifford algebra is generated by {1,e1,e2,e1e2}, the latter three generators squaring to −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

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTime1 day ago

    Added a few books:

    • Jayme Vaz, Jr., Roldão da Rocha, An introduction to Clifford algebras and spinors, Oxford University Press, 2019. xiv+242 pp. ISBN: 978-0-19-883628-5, 978-0-19-878292-6. DOI.

    • D. J. H. Garling, Clifford algebras: an introduction, London Mathematical Society Student Texts, 78. Cambridge University Press, Cambridge, 2011. viii+200 pp. ISBN: 978-1-107-42219-3. DOI.

    • Jacques Helmstetter, Artibano Micali, Quadratic mappings and Clifford algebras, Birkhäuser Verlag, Basel, 2008. xiv+504 pp. ISBN: 978-3-7643-8605-4. DOI.

    diff, v40, current

1 to 12 of 12

  1.