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Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes

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Abstract

An Adinkra is a graph from the study of supersymmetry in particle physics, but it can be adapted to study Clifford algebra representations. The graph in this context is called a Cliffordinkra, and puts some standard ideas in Clifford algebra representations in a geometric and visual context. In the past few years there have been developments in Adinkras that have shown how they are connected to error correcting codes, algebraic topology, algebraic geometry, and combinatorics. These connections also arise for Cliffordinkras. This paper introduces Cliffordinkras and describes the relationship to these subjects in that context. No previous knowledge of Adinkras and supersymmetry is assumed.

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Notes

  1. We use the same symbol \(\Gamma _i\) for the element of the Clifford algebra and for the matrix in its representation. The context will make clear which is meant.

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Acknowledgements

The author was partially supported by the endowment of the Ford Foundation Professorship of Physics at Brown University, and by the U.S. National Science Foundation grant PHY-1315155.

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  1. Natural Science Division, Pepperdine University, Malibu, CA, 90263-4321, USA

    Kevin Iga

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This article is part of the Topical Collection on Proceedings ICCA 12, Hefei, 2020, edited by Guangbin Ren, Uwe Kähler, Rafał  Abłamowicz, Fabrizio Colombo, Pierre Dechant, Jacques Helmstetter, G. Stacey Staples, Wei Wang.

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Iga, K. Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes. Adv. Appl. Clifford Algebras 31, 76 (2021). https://doi.org/10.1007/s00006-021-01181-0

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