2025/01/15 by Yuri Bazlov, Bazlov, Yuri, R. S. Chen +1
Physics and Astronomy · #Quantum Mechanics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2501.08942
A well-known noncommutative deformation \mathcal ANq of the polynomial algebra \mathcal AN can be obtained as a twist of \mathcal AN by a cocycle on the grading semigroup. Of particular interest to us is an interpretation of ANq 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 sn,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.