Geodesic
Cocycle deformations for weak Hopf algebras
Filomat, Tome 37 (2023) no. 26, p. 8725

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DOI

In this paper we introduce a theory of multiplication alteration by two-cocycles for weak Hopf algebras. We show that, just like it happens for Hopf algebras, if H a weak Hopf algebra and H σ its weak Hopf algebra deformation by a 2-cocycle σ, there is a braided monoidal category equivalence between the categories of left-right Yetter-Drinfel'd modules H YD H and H σ YD H σ. As a consequence we get in this context that the category Rep(D(H)) of left modules over the Drinfel'd double D(H) can be identified with the category Rep(D(H σ)) of left modules over the Drinfel'd double D(H σ).
DOI : 10.2298/FIL2326725A
Classification : 18D10, 16W30, 16T05
Keywords: Weak Hopf algebra, 2-cocycle, Yetter-Drinfel’d module, Drinfel’d double 
J N Alonsó Alvarez; J M Fernández Vilaboa; R González Rodríguez. Cocycle deformations for weak Hopf algebras. Filomat, Tome 37 (2023) no. 26, p. 8725 . doi: 10.2298/FIL2326725A
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     author = {J N Alons\'o Alvarez and J M Fern\'andez Vilaboa and R Gonz\'alez Rodr{\'\i}guez},
     title = {Cocycle deformations for weak {Hopf} algebras},
     journal = {Filomat},
     pages = {8725 },
     year = {2023},
     volume = {37},
     number = {26},
     doi = {10.2298/FIL2326725A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2326725A/}
}
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