A thin Lie algebra is a Lie algebra, graded over the positive integers, with its first homogeneous component of dimension two and generating, and such that each non-zero ideal of 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 (that is, the next diamond past) occurs in degree. We prove that if 5\$]]&gt;, then for some non-zero element of. In characteristic different from two this means is a sandwich element of. We discuss the relevance of this fact in connection with an important theorem of Premet on sandwich elements in modular Lie algebras.

Mattarei, S. (2022). A sandwich in thin lie algebras. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 65(1 (February 2022)), 136-145 [10.1017/S0013091521000845].

### A sandwich in thin lie algebras

#### Abstract

A thin Lie algebra is a Lie algebra, graded over the positive integers, with its first homogeneous component of dimension two and generating, and such that each non-zero ideal of 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 (that is, the next diamond past) occurs in degree. We prove that if 5\$]]>, then for some non-zero element of. In characteristic different from two this means is a sandwich element of. We discuss the relevance of this fact in connection with an important theorem of Premet on sandwich elements in modular Lie algebras.
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Articolo in rivista - Articolo scientifico
graded Lie algebra; Modular Lie algebra; sandwich; thin Lie algebra;
English
7-gen-2022
2022
65
1 (February 2022)
136
145
none
Mattarei, S. (2022). A sandwich in thin lie algebras. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 65(1 (February 2022)), 136-145 [10.1017/S0013091521000845].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/456821`
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