Preunits and weak crossed products

Neste artigo dase unha noción xeral de produto cruzado feble dunha álxebra A por un obxecto V, vivindo nunha categoría monoidal trenzada. A obtención deste tipo de produtos descansa na existencia dunha preunidade para a multiplicación, que se relaciona coa existencia de morfismos idempotentes. Asumindo que na categoría base os idempotentes rompen, a imaxe do idempotente asociado á preunidade herda a estrutura de produto cruzado dando lugar a unha álxebra. Como caso particular, recupérase a noción de produto cruzado dunha álxebra por unha biálxebra feble.The authors were supported by Xunta de Galicia (Project: PGIDT07PXB322079PR), Ministerio de Educación (Projects: MTM2007-62427, MTM2006-14908-CO2-01), and FEDER. Moreover, they would like to express their gratitude to the anonymous referee for the helpful comments and interesting questions that helped in improving this article.S

Weak C-cleft extensions, weak entwining structures and weak Hopf algebras

En este artigo formúlase a noción de extensión cleft feble para unha estructura entrelazante feble nunha categoría monoidal trenzada C. Próbase que, dada unha extensión deste tipo, se obtén unha xeneralización dun produto semidirecto a este contexto. Estes resultados permiten obter versións para álxebras de Hopf febles de resultados clásicos de álxebras de Hopf, como o teorema de Radford para álxebras de Hopf febles con proxección.The authors would like to thank the referee for his constructive and interesting comments. The authors have been supported by Ministerio de Ciencia y Tecnología, by Xunta de Galicia and by FEDER, Projects: BFM2003-07353-C02-01, BFM2003-07353-C02-02, PGIDITO4PXIC32202PN, PGIDITO4PXIC20703PN.S

Crossed Products in Weak Contexts

his version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10485-008-9139-2We define the general notion of crossed products in a weak context, which generalizes the ones defined by Blattner, Cohen and Montgomery, Doi and Takeuchi in the context of Hopf algebras and the one given by Brzezin´ ski. Also, the crossed products obtained by the authors, for weak Hopf algebras living in a symmetric monoidal category and weak C-cleft extensiMinisterio de Educación, proxectos MTM2007-62427, MTM2006-14908-CO2-01. Xunta de Galicia, proxecto PGIDT07PXB32-2079PR.S

Contact detection between a small ellipsoid and another quadric

[Abstract] We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This condition, named smallness condition, is a feature on the size and the shape of the quadrics and can be checked directly from their parameters. Under this hypothesis, contact can be noticed by means of the expressions in a discriminant system of the characteristic polynomial. Furthermore, relative positions can be classified through the sign of the coefficients of this polynomial. As an application of these results, a method to detect contact between a small ellipsoid and a combination of quadrics is given

Implementación de un sistema b-learning en la enseñanza práctica de Fisiopatología

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Impacto de la implementación del aprendizaje basado en problemas en combinación con las prácticas de laboratorio clínico y virtual de Fisiopatología para el desarrollo de competencias profesionales

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Implementación del aprendizaje basado en problemas (ABP) en la enseñanza práctica de la fisiología del sistema digestivo

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Adaptación a un entorno semipresencial de una nueva herramienta mixta del aprendizaje basado en problemas en combinación con las prácticas de laboratorio clínico a la nueva asignatura Bases Anatómicas y Fisiología del Cuerpo Humano

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Cohomological obstructions and weak crossed products over weak Hopf algebras

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGLet H be 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 → B we define its obstruction θσ as 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 → B such that H ⊗ B can be endowed with a weak crossed product structure with α keeping a cohomological-like relation with σ. Then, as a consequence, the class of the obstruction of σ vanish if, and only if, there exists a cleft extension of B by H.Agencia Estatal de Investigación | Ref. PID2020-115155GB-I0