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- W4206086876 abstract "Abstract A thin Lie algebra is a Lie algebra $L$ , graded over the positive integers, with its first homogeneous component $L_1$ of dimension two and generating $L$ , and such that each non-zero ideal of $L$ lies between consecutive terms of its lower central series. All homogeneous components of a thin Lie algebra have dimension one or two, and the two-dimensional components are called diamonds. Suppose the second diamond of $L$ (that is, the next diamond past $L_1$ ) occurs in degree $k$ . We prove that if $k>5$ , then $[Lyy]=0$ for some non-zero element $y$ of $L_1$ . In characteristic different from two this means $y$ is a sandwich element of $L$ . We discuss the relevance of this fact in connection with an important theorem of Premet on sandwich elements in modular Lie algebras." @default.
- W4206086876 created "2022-01-26" @default.
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- W4206086876 date "2022-01-07" @default.
- W4206086876 modified "2023-09-26" @default.
- W4206086876 title "A sandwich in thin lie algebras" @default.
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- W4206086876 doi "https://doi.org/10.1017/s0013091521000845" @default.
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