# Glasnik matematički,Vol. 54 No. 2, 2019.

Izvorni znanstveni članak
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

 Puni tekst: engleski, pdf (205 KB) str. 477-499 preuzimanja: 209* citiraj APA 6th EditionPham, 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 EditionPham, 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 EditionPham, 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 HarvardPham, 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 VancouverPham 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 IEEED.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.

Hrčak ID: 229607

Posjeta: 339 *