Generalized \(S\)-type Lie algebras. (English) Zbl 1135.17009
Summary: The generalized \(W\)-type Lie algebra \(W(e^{\pm x_1},\dots, e^{\pm x_m},m)\) has been introduced in the paper of the author [Southeast Asian Bull. Math. 26, No. 2, 245–255 (2002; Zbl 1056.17014)] using exponential functions.
We define generalized \(S\)-type Lie algebras \(S(e^{\pm x_1},\dots, e^{\pm x_m},m)\) over \(\mathbb F\) and \(S_p(e^{\pm x_1},\dots, e^{\pm x_m},m)\) over \(\mathbb F_p\). We show that the Lie algebras \(S(e^{\pm x_1},\dots, e^{\pm x_m},m)\) and \(S_p(e^{\pm x_1},\dots, e^{\pm x_m},m)\) are simple.
We define generalized \(S\)-type Lie algebras \(S(e^{\pm x_1},\dots, e^{\pm x_m},m)\) over \(\mathbb F\) and \(S_p(e^{\pm x_1},\dots, e^{\pm x_m},m)\) over \(\mathbb F_p\). We show that the Lie algebras \(S(e^{\pm x_1},\dots, e^{\pm x_m},m)\) and \(S_p(e^{\pm x_1},\dots, e^{\pm x_m},m)\) are simple.
MSC:
17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
17B65 | Infinite-dimensional Lie (super)algebras |
17B50 | Modular Lie (super)algebras |
Citations:
Zbl 1056.17014References:
[1] | J.E. Humphreys, Introduction to Lie algebras and representation theory , Springer-Verlag, New York, 1987, pp. 7-21. |
[2] | V.G. Kac, Description of filtered Lie algebra with which graded Lie algebras of Cartan type are associated , Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 832-834. |
[3] | N. Kawamoto, Generalizations of Witt algebras over a field of characteristic zero , Hiroshima Math. J. 16 (1986), 417-426. · Zbl 0607.17008 |
[4] | Ki-Bong Nam, Generalized \(W\) and \(H\) type Lie algebras , Algebra Colloq. 6 (1999), 329-340. · Zbl 0949.17007 |
[5] | ——–, Modular \(W\) and \(H\) type Lie algebras , Bull. of South Eastern Asian Math., vol. 26, Springer Verlag, New York, 2002, pp. 249-259. · Zbl 1056.17014 · doi:10.1007/s100120200046 |
[6] | A.N. Rudakov, Groups of automorphisms of infinite-dimensional simple Lie algebras , Math. USSR-Izv. 3 (1969), 707-722. · Zbl 0222.17014 · doi:10.1070/IM1969v003n04ABEH000798 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.