Geodesic
Central extensions of the Zassenhaus algebra and their irreducible representations
Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 457-474

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It is shown that the Zassenhaus algebra $W_1(m)$ over a field of characteristic $p>3$ has, up to equivalence, a unique nontrivial central extension $\widetilde{W}_1(m)$ (the modular Virasoro algebra). For the Virasoro algebra we construct a generalized Casimir element. All the irreducible $\widetilde{W}_1(m)$-modules are described. It is shown that there is no simple graded Lie algebra with zero component $L_0\cong\widetilde{W}_1(m)$. Bibliography: 15 titles. 
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     author = {A. S. Dzhumadil'daev},
     title = {Central extensions of the {Zassenhaus} algebra and their irreducible representations},
     journal = {Sbornik. Mathematics},
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     volume = {54},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_2_a9/}
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A. S. Dzhumadil'daev. Central extensions of the Zassenhaus algebra and their irreducible representations. Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 457-474. http://geodesic.mathdoc.fr/item/SM_1986_54_2_a9/