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Lie algebras graded by the weight systems \((\Theta_3,\mathrm{sl}_3)\) and \((\Theta_4,\mathrm{sl}_4)\). (English) Zbl 1523.17043

Eur. J. Math. 8, Suppl. 2, S765-S783 (2022); correction ibid. 8, Suppl. 2, S784 (2022).
Summary: A Lie algebra \(L\) is said to be \((\Theta_n,\mathrm{sl}_n)\)-graded if it contains a simple subalgebra \(\mathfrak{g}\) isomorphic to \(\mathrm{sl}_n\) such that \(L\) is generated by \(\mathfrak{g}\) as an ideal and the \(\mathfrak{g} \)-module \(L\) decomposes into copies of the adjoint module, the trivial module, the natural module \(V\), its symmetric and exterior squares \(S^2V\) and \(\wedge^2 V\), and their duals. In [the author, Generalized root graded Lie algebras. Ph.D. Thesis, University of Leicester (2018); A. Baranov and the author, J. Algebra 581, 1–44 (2021; Zbl 1478.17020)], we classified \((\Theta_n,\mathrm{sl}_n)\)-graded Lie algebras for \(n>4\). In this paper we describe the multiplicative structures and the coordinate algebras of \((\Theta_n,\mathrm{sl}_n)\)-graded Lie algebras for \(n=3,4\).
The erratum concerns a wrong reference citation in the original abstract.

MSC:

17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17B65 Infinite-dimensional Lie (super)algebras
17B70 Graded Lie (super)algebras
17B20 Simple, semisimple, reductive (super)algebras

Citations:

Zbl 1478.17020
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Full Text: DOI

References:

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