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

Bicovariant differential calculi for finite global quotients

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

Puni tekst: engleski, pdf (205 KB) str. 477-499 preuzimanja: 209* citiraj
APA 6th Edition
Pham, D.N. (2019). Bicovariant differential calculi for finite global quotients. Glasnik matematički, 54 (2), 477-499. https://doi.org/10.3336/gm.54.2.10
MLA 8th Edition
Pham, David N.. "Bicovariant differential calculi for finite global quotients." Glasnik matematički, vol. 54, br. 2, 2019, str. 477-499. https://doi.org/10.3336/gm.54.2.10. Citirano 28.10.2021.
Chicago 17th Edition
Pham, David N.. "Bicovariant differential calculi for finite global quotients." Glasnik matematički 54, br. 2 (2019): 477-499. https://doi.org/10.3336/gm.54.2.10
Harvard
Pham, D.N. (2019). 'Bicovariant differential calculi for finite global quotients', Glasnik matematički, 54(2), str. 477-499. https://doi.org/10.3336/gm.54.2.10
Vancouver
Pham DN. Bicovariant differential calculi for finite global quotients. Glasnik matematički [Internet]. 2019 [pristupljeno 28.10.2021.];54(2):477-499. https://doi.org/10.3336/gm.54.2.10
IEEE
D.N. Pham, "Bicovariant differential calculi for finite global quotients", Glasnik matematički, vol.54, br. 2, str. 477-499, 2019. [Online]. https://doi.org/10.3336/gm.54.2.10

Sažetak
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.

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

Hrčak ID: 229607

URI
https://hrcak.srce.hr/229607

Posjeta: 339 *