Leibniz representations of Lie algebras
The authors examine the category \(L({\mathfrak g})\) of finite-dimensional Leibniz representation [the authors, Math. Ann. 296, 139-158 (1993; Zbl 0821.17022)] of the finite-dimensional semisimple Lie algebra \({\mathfrak g}\). First, they notice that \(L({\mathfrak g})\) is not semisimple even when the characteristic of the field \(k\) is 0. One of the aims of the paper is to prove that this category has global dimension 2. Next, the authors obtain the description of the quiver of the category \(L({\mathfrak g})\) in the sense of \textit{P. Gabriel} [Manuscr. Math. 6, 71-103 (1962; Zbl 0232.08001)] and, in the end, they prove that this category is tame only for \(g= sl_2\), and give the complete list of indecomposable objects in that case.
category of finite-dimensional Leibniz representations
scientific article; zbMATH DE number 883767
scientific article