Wedderburn principal theorem for Jordan superalgebras. I. (English) Zbl 1423.17028
Summary: We consider finite dimensional Jordan superalgebras \(\mathfrak{J}\) over an algebraically closed field of characteristic 0, with solvable radical \(\mathcal{N}\) such that \(\mathcal{N} {}^2= 0\) and \(\mathfrak{J} / \mathcal{N}\) is a simple Jordan superalgebra of one of the following types: Kac \(\mathcal{K}_{10}\), Kaplansky \(\mathcal{K}_3\), superform or \(\mathcal{D}_t\).
We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subbimodules of \(\mathcal{N}\) are imposed, where \(\mathcal{N}\) is considered as a \(\mathfrak{J} / \mathcal{N}\)-bimodule. Using counterexamples, it is shown that the imposed restrictions are essential.
We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subbimodules of \(\mathcal{N}\) are imposed, where \(\mathcal{N}\) is considered as a \(\mathfrak{J} / \mathcal{N}\)-bimodule. Using counterexamples, it is shown that the imposed restrictions are essential.
MSC:
| 17C70 | Super structures |
Keywords:
Jordan superalgebras; Wedderburn theorem; decomposition theorem; semisimple Jordan superalgebrasReferences:
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