Star-product on complex sphere $\mathbb{S}^{2n}$

TL;DR

This paper constructs a $U_q(so(2n+1))$-equivariant star-product on the complex sphere $S^{2n}$, providing a quantum deformation of the classical geometric structure.

Contribution

It introduces a novel $U_q(so(2n+1))$-equivariant local star-product on the complex sphere as a non-Levi conjugacy class.

Findings

Explicit construction of the star-product.

Establishment of equivariance under quantum group actions.

Application to noncommutative geometry of complex spheres.

Abstract

We construct a $U_q(\mathrm{so}(2n+1))$-equivariant local star-product on the complex sphere $\mathbb{S}^{2n}$ as a Non-Levi conjugacy class $SO(2n+1)/SO(2n)$.