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Annales de l’Institut Henri Poincaré D

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Volume 4, Issue 3, 2017, pp. 387–415
DOI: 10.4171/AIHPD/43

Published online: 2017-09-26

An application of cubical cohomology to Adinkras and supersymmetry representations

Charles F. Doran[1], Kevin M. Iga[2] and Gregory D. Landweber[3]

(1) University of Alberta, Edmonton, Canada
(2) Pepperdine University, Malibu, USA
(3) Bard College, Annandale-on-Hudson, USA

An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincaré algebra. The markings on the vertices and edges of an Adinkra are cochains for cubical cohomology. This article explores the cubical cohomology of Adinkras, treating these markings analogously to characteristic classes on smooth manifolds.

Keywords: Cubical cohomology, supersymmetry, Adinkras, signed graphs

Doran Charles, Iga Kevin, Landweber Gregory: An application of cubical cohomology to Adinkras and supersymmetry representations. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 4 (2017), 387-415. doi: 10.4171/AIHPD/43