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We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but suffcient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras. Our result is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov's theorem for type P(N). We also obtain a generalization of Kac's coordinatization via Tits-Kantor-Koecher construction. Actually, the motivation of this generalization comes from the Fermionic-Bosonic module construction. 相似文献
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设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+φ(A),这里T∈B(X),φ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有φ(A+B)=φ(A),其中B是交换子的和. 相似文献
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We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner. 相似文献
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Pabitra Kumar Pradhan Manoj Kumar Pandey 《Mathematical Methods in the Applied Sciences》2020,43(9):6081-6092
The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one- and two-dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one-dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour. 相似文献
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《Physics letters. A》2020,384(17):126349
We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra. 相似文献
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We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ?. In particular, we describe all irreducible components of these varieties. 相似文献
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Nowadays, pharmaceutical antibiotics are known as a serious class of pollutants. Therefore, it is important to develop effective methods for removing these pollutants from aqueous media. Different methods were applied for this purpose, and among these methods, chemical reduction by a cheap and eco‐friendly nanocatalyst is the most efficient and simplest method. In this research, based on graphene oxide supported by zero‐valent iron in mono‐, bi‐, and tri‐metallic systems, various nanocomposites were synthesized and used to degrade tetracycline as a model antibiotic from aqueous media. An investigation was carried out on the synergic effect among graphene oxide and the nano zero‐valent iron‐based tri‐metallic system as well as removal efficiencies. It was found that higher degradation efficiency is yielded by graphene oxide supported by Fe/Cu/Ag tri‐metallic system. The maximum synergic effect occurs at an acidic medium. The Brunauer–Emmett–Teller, Fourier transform spectroscopy, scanning electron microscopy‐energy dispersive X‐ray analysis, transmission electron microscopy, and X‐ray diffraction analysis were used to characterize the synthesized nanocomposites, which has successfully proved the loading of nanoscale Fe/Cu/Ag tri‐metallic on a graphene oxide support. The central composite design was used to model and optimize all involved variables affecting antibiotic removal efficiency. The consequences illustrated the optimum condition regarding the removal of 50 ppm of tetracycline, for the nanocomposites dose of 3.0 mg ml?1, the contact time of 30 min, and pH of 2, was achieved using the simplex non‐linear optimization method. Moreover, antibiotic adsorption kinetic models were also investigated. Finally, the tetracycline removal from aqueous media at different concentrations, 25, 50, and 75 ppm, was successful by applying the proposed nanocomposite, and the results showed tetracycline removal efficiencies of above 70%. 相似文献