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Quantum Segre maps via cocycle twists

Authors :
Bazlov, Yuri
Chen, Runyang
Publication Year :
2025

Abstract

A well-known noncommutative deformation $\mathcal A^N_{\mathbf{q}}$ of the polynomial algebra $\mathcal A^N$ can be obtained as a twist of $\mathcal A^N$ by a cocycle on the grading semigroup. Of particular interest to us is an interpretation of $A^N_{\mathbf{q}}$ as a quantum projective space. We outline a general method of cocycle twist quantization of tensor products and morphisms between algebras graded by monoids and use it to construct deformations of the classical Segre embeddings of projective spaces. The noncommutative Segre maps $s_{n,m}$, proposed by Arici, Galuppi and Gateva-Ivanova, arise as a particular case of our construction which corresponds to factorizable cocycles in the sense of Yamazaki.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2501.08942
Document Type :
Working Paper