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We give a detailed study of the enveloping algebra of the Lie superalgebra sl(2, 1), including classification of irreducible HarishChandra modules, completeness of finite dimensional irreducible, explicit computation of center, and classification of primitive ideals.Introduction and main results. Lie superalgebras are important both in physics and in mathematics [5]. In physics, they are used e.g. to unify fermions and bosons in a unique picture (one irreducible representation of the structure) via supersymmetry. In mathematics, their enveloping algebras provide a class of very interesting noetherian algebras. Much information is known about enveloping algebras of Lie algebras (e.g., [4]), but for superalgebras there is a lot to do (see e.g.[2] for a pioneering work, and [13] for a very nice survey of results obtained up to now). Let us restrict to the simple case; then a natural distinction does appear between simple superalgebras with an enveloping algebra which is a domain and others. The first case is exactly the series osp(l, 2ή), which are also the only semi-simple simple superalgebras [8]. The simplest model of this case is h = osp(l, 2) U(h) was completely studied in [16], including explicit computation of Prim U(h). The simplest model of the second case is g = sl(2, 1), and the purpose of the present paper is a complete study of U(g). We shall give a classification of irreducible Harish-Chandra modules, a detailed computation of the center Z(g) of U(g), and a classification of Prim U(g).Let us recall known results: finite dimensional irreducible representations of g = sl(2, 1) are known [18], and also unitary irreducible are classified ([6], [7]). Moreover, finite dimensional representations provide a complete set of representations [2], but are generally not fully reducible.A fundamental result of our paper is the fact that finite dimensional irreducible provide a complete set, because of information that can be deduced on U(g). Actually, we deduce an explicit determination of the center Z(g), which shows that Z{g) is not a finitely

Ni−Cu−Al layered double hydroxide (Ni−Cu−Al LDH) was proposed as an electro‐Fenton‐like catalyst for 8‐hydroxyquinoline‐5‐sulfonic acid (8‐HQS) removal in water. The properties of the prepared catalysts were characterized by using X‐ray, SEM and EDAX analyses. The effect of numerous operative parameters on the removal of 8‐HQS and total organic carbon (TOC) was studied. Very high level removal of both 8‐HQS and TOC (87 and 79 %, respectively) were obtained by using a pressurized electro‐Fenton‐like process (PrEFL‐LDH) at P=10 bars, using a Ti/IrO2‐Ta2O5 anode for 6 h. The process presented good performances in a large range of pH (3–10) and gave better removals of 8‐HQS and TOC with respect to that achieved by both i) EF catalyzed by homogeneous (FeSO4) or natural heterogeneous catalysts (pyrite and chalcopyrite) and ii) anodic oxidation at a boron doped diamond anode. Ni−Cu−Al LDH retained its catalytic activity after four cycles. Moreover, the carboxylic acid intermediates were identified and analyzed by HPLC.

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Bisphenol A (BPA), an endocrine disrupting compound, is of concern because of its wide presence throughout the environment and its harmful effects. The present study aimed to prepare an eco-friendly, low-cost, and efficient adsorbent for removal of BPA from wastewater. A natural Tunisian clay was used as a raw material. First, the clay was purified and then modified with hexadecyltrimethylammonium bromide (HDTMA) using microwave heating. The optimal conditions for clay modification were as follows: activation ratio = 0.3:(g/g), solid/liquid ratio = 5%, and microwave heating condition (2:min, 100:W). The purified and modified clays, abbreviated as HP and HMH, respectively, were characterized by scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), and nitrogen adsorption/desorption analysis (BET). Adsorption tests were conducted in a batch reactor process under various conditions. The tests showed that the BET specific surface area of HMH is considerably smaller than that of HP, whereas the basal spacing increased from 14.99 to 22.07 Å after modification, indicating the success of HP organophilization. The adsorption of BPA onto HMH was not affected by the pH of solution between 2 and 10 and only slightly by temperature variation from 23 to 50°C, but was affected significantly by the initial concentration of BPA, contact time, and organo-clay dose. At equilibrium, the data obtained were fitted to Langmuir and Freundlich models. The best fit was obtained by the Langmuir model with a maximum monolayer adsorption capacity of 217.39 mg/g at 23°C. The thermodynamic study suggested that the removal of BPA by HMH was spontaneous (ΔG < 0), exothermic (ΔH < 0), and favorable. The present study demonstrated that HMH synthesized from an abundant and cheap natural clay could be used successfully as a low-cost adsorbent for the removal of BPA from wastewater.

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