Original scientific paper

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

Bicovariant differential calculi for finite global quotients

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

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 \(\Bbbk(G\ltimes M)\simeq \Bbbk[G\ltimes M]^\ast\), where \(G\ltimes M\) is the action groupoid associated to \((M,G)\), and \(\Bbbk[G\ltimes M]\) is the groupoid algebra of \(G\ltimes M\). Specifically, we prove a necessary and sufficient condition for a FODC over \(\Bbbk(G\ltimes M)\) to be bicovariant and then show that the isomorphism classes of bicovariant FODCs over \(\Bbbk(G\ltimes M)\) 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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