(Finite) presentations of the Albert-Frank-Shalev Lie algebras
Carrara, Claretta
Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 391-427 / Harvested from Biblioteca Digitale Italiana di Matematica
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In questo lavoro vengono studiate le algebre di Albert-Frank-Shalev. Queste sono algebre di Lie modulari di dimensione infinita, ottenute da un loop di certe algebre semplici di dimensione finita. Si dimostra che le algebre di Albert-Frank-Shalev sono unicamente determinate, a meno di elementi centrali o secondo centrali, da un certo quoziente finito-dimensionale. Tale risultato si ottiene dando la presentazione finita di un'algebra il cui quoziente sul secondo centro (infinito-dimensionale) è isomorfo alle algebre di Albert-Frank-Shalev.

Publié le : 2001-06-01
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     author = {Claretta Carrara},
     title = {(Finite) presentations of the Albert-Frank-Shalev Lie algebras},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {391-427},
     zbl = {1177.17018},
     mrnumber = {1831996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_2_391_0}
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Carrara, Claretta. (Finite) presentations of the Albert-Frank-Shalev Lie algebras. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 391-427. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_2_391_0/

[AF55] Albert, A. A. and Frank, M. S., Simple Lie algebras of characteristic p, Univ. e Politec. Torino. Rend. Sem. Mat., 14 (1954-55), 117-139. | MR 79222 | Zbl 0065.26801

[Bla58] Blackburn, N., On a special class of p-groups, Acta Math., 100 (1958), 45-92. | MR 102558 | Zbl 0083.24802

[C99] Carrara, C., Central extensions of Albert-Frank-Shalev Lie algebras, in preparation (1999).

[CMN97] Caranti, A.-Mattarei, S.-Newman, M. F., Graded Lie algebras of maximal class, Trans. Amer. Math. Soc., 349, no. 10 (1997), 4021-4051. | MR 1443190 | Zbl 0895.17031

[CN99] Caranti, A.-Newman, M. F., Graded Lie algebras of maximal class. II, J. Algebra, 229, no. 2 (2000), 750-784. | MR 1769297 | Zbl 0971.17015

[HNO95] Havas, G.-Newman, M. F.-O'Brien, E. A., ANU p-Quotient Program, Version 1.2, written in C, available from maths.anu.edu.au by anonymous ftp in the directory /pub/PQ, as a share library with GAP 3.4 and as part of Magma (1995).

[Jur99] Jurman, G., Graded Lie algebras of maximal class. III, in preparation (1999). | Zbl 1058.17020

[Kos96] Kostrikin, Alexei I., The beginnings of modular Lie algebra theory, Group theory, algebra, and number theory (Saarbrücken, 1993) (Berlin), de Gruyter, Berlin (1996), 13-52. | MR 1440203 | Zbl 0874.17021

[Luc78] Lucas, E., Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques, suivant un module premier, Bull. Soc. Math. France, 6 (1878), 49-74. | JFM 10.0139.04 | MR 1503769

[Rob82] Robinson, John Scott, A course in the theory of groups, Graduate Texts in Mathematics, Springer-Verlag, New York, 80 (1982). | MR 648604 | Zbl 0483.20001

[S+95] Schönert, M. ET AL., GAP - Groups, Algorithms and Programming, Release 3.4, Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany (1995).

[Sha94] Shalev, Aner, Simple Lie algebras and Lie algebras of maximal class, Arch. Math. (Basel), 63, no. 4 (1994), 297-301. | MR 1290602 | Zbl 0803.17006

[Sha95] Shalev, A., Finite p-groups, Finite and locally finite groups (Istanbul, 1994) (Dordrecht), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ., 471 (1995), 401-450. | MR 1362818 | Zbl 0839.20028