Braided Supersymmetry and (CO-)HOMOLOGY

Details Braided Supersymmetry and (CO-)HOMOLOGY Braided Supersymmetry and (CO-)HOMOLOGY

1994-09-23

arxiv.org/abs/hep-th/9409136v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, plain TEX (with input of amssym.def, amssym.tex and local amstex), UVA-FWI-Report 94-18

Scientific paper

Within the framework of braided or quasisymmetric monoidal categories braided Q-supersymmetry is investigated, where Q is a certain functorial isomorphism in a braided symmetric monoidal category. For an ordinary (co-)quasitriangular Hopf algebra (H,R) a braided monoidal category of H-(co-)modules with braiding induced by the R-matrix is considered. It can be shown for a specific class of Q-supersymmetries in this category that every braided Q-super-Hopf algebra B admits an ordinary Q-super-Hopf algebra structure on the cross product BxH such that H is a sub-Hopf algebra and B is a subalgebra in BxH. Applying this Q-bosonization to the quantum Koszul complex (K(q,g),d) of the quantum enveloping algebra Uq(g) for Lie algebras g associated with the root systems A, B, C and D one obtains a classical super-Hopf algebra structure on (K(q,g),d) where the structure maps are morphisms of modules with differentiation.

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