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- W4287602928 abstract "Thin Lie algebras are infinite-dimensional graded Lie algebras $L=bigoplus_{i=1}^{infty}$, with $dim(L_1)=2$ and satisfying a covering property: for each $i$, each nonzero $zin L_i$ satisfies $[zL_1]=L_{i+1}$. It follows that each homogeneous components $L_i$ is either one- or two-dimensional, and in the latter case is called a diamond. Hence $L_1$ is a diamond, and if there are no other diamonds then $L$ is a graded Lie algebra of maximal class. We present simpler proofs of some fundamental facts on graded Lie algebras of maximal class, and on thin Lie algebras, based on a uniform method, with emphasis on a polynomial interpretation. Among else, we determine the possible values for the most fundamental parameter of such algebras, which is the dimension of their largest metabelian quotient." @default.
- W4287602928 created "2022-07-25" @default.
- W4287602928 creator A5087849922 @default.
- W4287602928 date "2020-11-08" @default.
- W4287602928 modified "2023-09-29" @default.
- W4287602928 title "Constituents of graded Lie algebras of maximal class and chain lengths of thin Lie algebras" @default.
- W4287602928 doi "https://doi.org/10.48550/arxiv.2011.04110" @default.
- W4287602928 hasPublicationYear "2020" @default.
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