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On Non Commutative Calabi-Yau Hypersurfaces

A. Belhaj·E. H. Saidi
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Abstract

Using the algebraic geometry method of Berenstein et al (hep-th/0005087), we reconsider the derivation of the non commutative quintic algebra ${\mathcal{A}}_{nc}(5)$ and derive new representations by choosing different sets of Calabi-Yau charges ${C_{i}^{a}}$. Next we extend these results to higher $d$ complex dimension non commutative Calabi-Yau hypersurface algebras ${\mathcal{A}}_{nc}(d+2)$. We derive and solve the set of constraint eqs carrying the non commutative structure in terms of Calabi-Yau charges and discrete torsion. Finally we construct the representations of ${\mathcal{A}}_{nc}(d+2) $ preserving manifestly the Calabi-Yau condition $ \sum_{i}C_{i}^{a}=0$ and give comments on the non commutative subalgebras.

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A. Belhaj, E. H. Saidi. 2001-11-28. On Non Commutative Calabi-Yau Hypersurfaces. https://doi.org/10.1016/s0370-2693(01)01317-x

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