query: Example of a Lie algebra such that the form killing $ K_{\mathfrak g} = 0 $ but $\mathfrak g$ is not nilpotent
positive_passages.docid: 24249
positive_passages.text: When is the Killing form null?
negative_passages.docid: 147148
negative_passages.text: why is $S^2$ not a Lie group?
negative_passages.docid: 121257
negative_passages.text: Image of Homomorphism of Lie groups
negative_passages.docid: 73662
negative_passages.text: Example of non-flat modules
negative_passages.docid: 19996
negative_passages.text: Example where union of increasing sigma algebras is not a sigma algebra
negative_passages.docid: 93358
negative_passages.text: Find an example of a non-surjective field endomorphism
negative_passages.docid: 87922
negative_passages.text: Computing the Lie bracket on the Lie group $GL(n, \mathbb{R})$
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 101229
negative_passages.text: Lie algebra of $\left(\begin{smallmatrix}a & b\\ & a^2\end{smallmatrix}\right )$ in $GL_2(\mathbb{R})$
negative_passages.docid: 51889
negative_passages.text: How to "find" this Lie algebra: proof that $\mathfrak{sl}$ is trace zero matrices
negative_passages.docid: 130268
negative_passages.text: How to prove that a nilpotent matrix is not invertible?
negative_passages.docid: 63882
negative_passages.text: Show that the heisenberg group is nilpotent
negative_passages.docid: 13292
negative_passages.text: Which of $\{J_0,J_1,J_2\}$ and $\{J_0,J_+,J_-\}$ is a generator for the Lie algebra $\mathfrak{su}(2)$?
negative_passages.docid: 24131
negative_passages.text: How to visualise the derived series of the Lie algebra $\mathfrak{u}(n,\mathbb{C})$?
negative_passages.docid: 107594
negative_passages.text: Lie bracket for Lie algebra of $SO(n,m)$
negative_passages.docid: 62219
negative_passages.text: Under what conditions is the exponential map on a Lie algebra injective?
negative_passages.docid: 133495
negative_passages.text: Example of a ring without Invariant Basis Property