Spinors in braided geometry

• Autorzy: Mićo Đurđević , Zbigniew Oziewicz
• Języki publikacji: EN

Abstrakty

EN

Let V be a ℂ-space, $σ ∈ End(V^{⊗2})$ be a pre-braid operator and let $F ∈ lin(V^{⊗2},ℂ).$ This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra $Cl(V,σ,0) ≡ V^{∧}(σ)$. If $σ ≠ σ^{-1}$ and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation is faithful and irreducible.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 315-325

Daty

wydano

1996

Twórcy

autor

Mićo Đurđević

• Instituto de Matematicas, UNAM, Area de la Investigacion Cientifica, Circuito Exterior, Ciudad Universitaria, México DF, CP 04510 México

autor

Zbigniew Oziewicz

• Facultad de Estudios Superiores Cuautitlan, UNAM, Apartado Postal , #25 Cuautitlan Izcalli, CP 54700, México

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