RT Journal Article
T1 Cohomological obstructions and weak crossed productus over weak Hopf algebras
A1 González Rodríguez, Ramón
A1 Rodríguez Raposo, Ana Belén
K1 Weak Hopf algebras
K1 Sweedler cohomology
K1 Weak crossed products
K1 Cleft extensions
K1 Obstruction
AB Let Hbe a cocommutative weak Hopf algebra and let (B, ϕB)a weak left H-module algebra. In this paper, for a twisted convolution invertible morphism σ:H2→Bwe define its obstruction θσas a Sweedler 3-cocycle with values in the center of B. We obtain that the class of this obstruction vanish in third Sweedler cohomology group H3ϕZ(B)(H, Z(B))if, and only if, there exists a twisted convolution invertible 2-cocycle α :H2→Bsuch that H⊗Bcan be endowed with a weak crossed product structure with αkeeping a cohomological-like relation with σ. Then, as a consequence, the class of the obstruction of σvanish if, and only if, there exists a cleft extension of Bby H.
PB Elsevier
SN 0021-8693
YR 2022
FD 2022
LK http://hdl.handle.net/10347/32429
UL http://hdl.handle.net/10347/32429
LA eng
NO Ramón González Rodríguez, Ana Belén Rodríguez Raposo, Cohomological obstructions and weak crossed products over weak Hopf algebras, Journal of Algebra, Volume 610, 2022, Pages 491-526, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2022.07.030.
NO The authors were supported by Ministerio de Ciencia e Innovación of Spain. Agencia Estatal de Investigación. Unión Europea - Fondo Europeo de Desarrollo Regional (FEDER). Grant PID2020-115155GB-I00: Homología, homotopía e invariantes categóricos en grupos y álgebras no asociativas.
DS Minerva
RD 28 abr 2026