Spectral triples with multitwisted real structure

Journal of noncommutative geometry

article

Ludwik Dąbrowski¹  Andrzej Sitarz² 

[1] SISSA;Jagiellonian University

关键词: Noncommutative geometry;    spectral triples;   

DOI  :  10.4171/jncg/450

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

We generalize the notion of spectral triple with reality structure to spectral triples with multitwisted real structure, the class of which is closed under the tensor product composition. In particular, we introduce a multitwisted first-order condition (characterizing the Dirac operators as an analogue of first-order differential operator). This provides a unified description of the known examples, which include rescaled triples with the conformal factor from the commutant of the algebra and (on the algebraic level) triples on quantum disc and on quantum cone, that satisfy twisted first-order condition of Brzeziński et al. (2016, 2019), as well as asymmetric tori, non-scalar conformal rescaling and noncommutative circle bundles. In order to deal with them, we allow twists that do not implement automorphisms of the algebra of spectral triple.

【 授权许可】

CC BY