Ruibin Zhang: Noncommutative spaces for parafermions
发布日期:2024-07-01  字号:   【打印



:Ruibin Zhang 教授

工作单位University of Sydney



We introduce a class of non-commutative spaces, referred to as paramanifolds, which provide a natural setting for Green’s parafermions in the same way as supermanifolds for fermions.  They are ringed spaces with the structure sheaves being sheaves of para-algebras. For any given supermanifold X, there is a family of para-manifolds X(p) for positive integers p, such that X(1) recovers the supermanifold itself. A differential analysis on paramanifolds is developed, which can be readily applied to model physical problems. The affine paraspaces and projective paraspaces are treated in detail as examples. This talk is based on the paper R.B. Zhang, Noncommutative spaces for parafermions. J. Geom. Phys. 201 (2024) Article 105192.


Ruibin Zhang,澳大利亚悉尼大学数学与统计学院教授,澳大利亚数学会副主席。曾获得澳大利亚研究委员会伊丽莎白二世奖学金,澳大利亚研究委员会教授奖等诸多荣誉。研究主要集中在李理论及其在量子物理中的应用,涉及量子(超)群、李超代数、低维拓扑、非交换几何等领域。特别地,在量子代数的结构和表示理论等方面取得了一系列有重要国际影响的研究成果,在包括国际数学顶尖期刊Annals of Mathematics, J.Eur.Math.Soc., Adv.Math, Comm.Math.Phys, Proc.Lond.Math.Soc等重要国际数学刊物上发表140多篇高水平论文,并被国际同行大量引用。