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The derivation algebra of the Cartan-type Lie superalgebra \(HO\). (English) Zbl 1162.17308

Summary: The Cartan-type Lie superalgebra \(HO\) over a field of prime characteristic is considered in this paper. We first investigate generators of \(HO\). Then we give a detailed description of the \(\mathbb Z\)-homogeneous derivations of \(HO\). As a result, we obtain that \[ \text{Der}\, HO=\text{ad}(\overline{HO}*\mathbb F\cdot h)\oplus\text{span}_{\mathbb F}\{(\text{ad}\, D_i)^{p^k_i}\mid i\in Y_0,\;1\leq k_i<t_i\}. \] Finally, the outer derivation algebra \(\text{Der}_{\text{out}}(HO)\) is completely determined.

MSC:

17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
17B50 Modular Lie (super)algebras
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