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nLab > Latest Changes: ten-fold way

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 6th 2023

    starting something (following discussion here)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 6th 2023

    Added

    It includes the comment

    A key point we want to stress is that the 10-fold way is usually viewed as 10 = 2+8, where 2 and 8 are the periodicities in complex and real K-theory. And then the K-theory classification of topological phases is criticized because it only applies to free systems. However, we believe this viewpoint is slightly misguided. The unifying concept is really that of a real super-division algebra, and there are 10 such. They can be parceled into 10 = 8+2 but they can also equally naturally be parceled into 10 = 7+3 (with the 3 referring to the purely even superdivision algebras).

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 6th 2023

    Added

    Moore argues (Moore 13, p. 129) that the proper basis of the 10-fold way is the classification of real super-division algebras, and conjectures a 1-1 correspondence between these and Dyson’s 10 types (p. 132).

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 6th 2023

    Added that he established the correspondence with Geiko in

    • {#GeikoMoore21} Dyson’s classification and real division superalgebras, April 2021, Journal of High Energy Physics 2021(4):299, ([http://dx.doi.org/10.1007/jhep04(2021)299](DOI: 10.1007/jhep04(2021)299)).

    diff, v2, current

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