Twisting Hopf algebras from cocycle deformations

Let $H$ be a Hopf algebra. Any finite-dimensional lifting of $V\in {}^{H}_{H}\mathcal{YD}$ arising as a cocycle deformation of $A=\mathfrak{B}(V)\#H$ defines a twist in the Hopf algebra $A^*$, via dualization. We follow this recipe to write down explicit examples and show that it extends known techniques for defining twists. We also contribute with a detailed survey about twists in braided categories.Comment: 20 page

Liftings of Nichols algebras of diagonal type III. Cartan type G2G_2

We complete the classification of Hopf algebras whose infinitesimal braiding is a principal Yetter-Drinfeld realization of a braided vector space of Cartan type $G_2$ over a cosemisimple Hopf algebra. We develop a general formula for a class of liftings in which the quantum Serre relations hold. We give a detailed explanation of the procedure for finding the relations, based on the recent work of Andruskiewitsch, Angiono and Rossi Bertone.Comment: 54 pages; including an appendix. Final version, to appear in J. Algebr

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Determinación analítica de fármacos con propiedades antiepilépticas

The necessity of disposable biosensors for simple, rapid and inexpensive analysis in fields such as clinical, environmental or industrial has been highlighted over the past decade. In this way, screen-printed electrodes (SPEs) have been shown as inexpensive and reproducible devices for mass production of miniaturized biosensors [1-4]. These transducers, building by sequential layer deposition on the surface of ceramic or plastic substrates and curing steps, have been conventionally linked to the sensing element by adsorption, cross-linking, electropolymerization or covalent bonding. Bioelements are commonly immobilized after the printing and firing processes, because of the high temperatures reached during the curing step [5]. The immobilization procedure requires maintaining the initial properties of the enzyme intact. Thus, successful developments of biosensors largely rely on the cost and stability of the sensing elements [3]. Even if the above-mentioned immobilization procedures are efficient, they imply additional steps after fabrication of the screen-printed carbon electrodes (SPCEs), which extends the whole biosensor manufacturing. Screen-printing techniques also offer another attractive immobilization procedure consisting of printing the biological material. Enzymes, which are proteins able to catalyse specific chemical reactions in vivo, are by far the most commonly employed bioelements [1]. Enzymes can be integrated into the ink to form the sensing paste, which can be screen-printed resulting in biosensors fabricated by only one technology [6-8]. Undoubtedly, this immobilization procedure, which is known as automated immobilization, is particularly interesting for mass production of disposable biosensors. This work presents a simple way for preparing SPCEs modified with Horseradish peroxidase (HRP) for the determination of Levetiracetam (LEV). This second-generation antiepileptic drug (AEDs) has been previously determined using a SPCE-biosensor based on the immobilization of Horseradish peroxidase (HRP) by pyrrole electropolymerization [9] and covalent bonding [10] The screen-printing of HRP-containing ink (SPCHRPEs) offers a higher rapidity and simplicity in the manufacturing process of biosensors for LEV determination