# Spinors in braided geometry

Mićo Đurđević; Zbigniew Oziewicz

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 315-325
- ISSN: 0137-6934

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topĐurđević, Mićo, and Oziewicz, Zbigniew. "Spinors in braided geometry." Banach Center Publications 37.1 (1996): 315-325. <http://eudml.org/doc/208608>.

@article{Đurđević1996,

abstract = {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.},

author = {Đurđević, Mićo, Oziewicz, Zbigniew},

journal = {Banach Center Publications},

keywords = {Clifford algebras; spinor representations; braided geometry; braided exterior algebra; Hopf algebra; braided derivation; braided Chevalley deformation; quantum Yang Baxter equation; Grassmann algebra},

language = {eng},

number = {1},

pages = {315-325},

title = {Spinors in braided geometry},

url = {http://eudml.org/doc/208608},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Đurđević, Mićo

AU - Oziewicz, Zbigniew

TI - Spinors in braided geometry

JO - Banach Center Publications

PY - 1996

VL - 37

IS - 1

SP - 315

EP - 325

AB - 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.

LA - eng

KW - Clifford algebras; spinor representations; braided geometry; braided exterior algebra; Hopf algebra; braided derivation; braided Chevalley deformation; quantum Yang Baxter equation; Grassmann algebra

UR - http://eudml.org/doc/208608

ER -

## References

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- [14] Z. Oziewicz, Clifford algebra for Hecke braid, in: Clifford Algebras and Spinor Structures, R. Ablamowicz and P. Lounesto (ed.), Mathematics and Its Applications vol. 321, Kluwer Academic Publishers, Dordrecht 1995, pp. 397-411. Zbl0845.15011
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