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:
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| [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 |
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