A family of transitive modular Lie superalgebras with depth one期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A family of transitive modular Lie superalgebras with depth one

Authors:

Affiliation:

1. Department of Mathematics, Harbin Normal University, Harbin 150080, China
2. Department of Mathematics, Northeast Normal University, Changchun 130024, China

Abstract:

The embedding theorem is established for ℤ-graded transitive modular Lie superalgebras $\mathfrak{g} = \oplus _{ - 1 \leqslant i \leqslant r} \mathfrak{g}_i$ satisfying the conditions:

(i)	$\mathfrak{g}_0 \simeq \tilde p(\mathfrak{g}_{ - 1} )$ and $\mathfrak{g}_0$ -module $\mathfrak{g}_{ - 1}$ is isomorphic to the natural $\tilde p(\mathfrak{g}_{ - 1} )$ -module;
(ii)	$\mathfrak{g}_{ - 1} = \tfrac{2}{3}n(2n^2 + 1)$ , where $n = \tfrac{1}{2}$ dim $\mathfrak{g}_{ - 1}$ .

In particular, it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras. The restricted Lie superalgebras are also considered. This work is partially supported by the National Natural Science Foundation of China (Grant No. 10671160) and China Postdoctoral Science Foundation (Grant No. 200604001)

Keywords:

flag divided power algebra modular Lie superalgebra embedding theorem

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