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Original scientific paper

https://doi.org/10.3336/gm.54.2.10

Bicovariant differential calculi for finite global quotients

David N. Pham orcid id orcid.org/0000-0001-5615-0719 ; Department of Mathematics & Computer Science, Queensborough C. College, City University of New York, Bayside, NY 11364, USA


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Abstract

Let (M,G) be a finite global quotient, that is, a finite set M with an action by a finite group G. In this note, we classify all bicovariant first order differential calculi (FODCs) over the weak Hopf algebra k(GM)k[GM], where GM is the action groupoid associated to (M,G), and k[GM] is the groupoid algebra of GM. Specifically, we prove a necessary and sufficient condition for a FODC over k(GM) to be bicovariant and then show that the isomorphism classes of bicovariant FODCs over k(GM) are in one-to-one correspondence with subsets of a certain quotient space.

Keywords

Global quotients; noncommutative differential geometry; first order differential calculi; weak Hopf algebras

Hrčak ID:

229607

URI

https://hrcak.srce.hr/229607

Publication date:

11.12.2019.

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