query: Adjoint representation, standard basis - $\mathfrak{sl}(2)$ and Killing form
positive_passages.docid: 146690
positive_passages.text: Basis for adjoint representation of $sl(2,F)$
negative_passages.docid: 107594
negative_passages.text: Lie bracket for Lie algebra of $SO(n,m)$
negative_passages.docid: 12698
negative_passages.text: Orthonormal basis for $\mathcal{L}^2([0,1])$
negative_passages.docid: 117737
negative_passages.text: Why is $\mathfrak{sl}(n)$ the algebra of traceless matrices?
negative_passages.docid: 118117
negative_passages.text: Conjugacy Class in a matrix group with columns of standard basis
negative_passages.docid: 34886
negative_passages.text: Transvection matrices generate $ \operatorname{SL}_n(\mathbb{R}) $
negative_passages.docid: 48524
negative_passages.text: Existence proof of the tensor product using the Adjoint functor theorem.
negative_passages.docid: 62832
negative_passages.text: What is the Killing form of $\mathfrak{gl}_{m}$?
negative_passages.docid: 121449
negative_passages.text: An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
negative_passages.docid: 136791
negative_passages.text: Associative Lie algebra
negative_passages.docid: 105322
negative_passages.text: Computing the quotient of SL(2,Z) by its commutator subgroup
negative_passages.docid: 119352
negative_passages.text: compact and self adjoint square root of an operator
negative_passages.docid: 112216
negative_passages.text: Geometric description of canonical commutation relation
negative_passages.docid: 86224
negative_passages.text: The root system of $sl(3,\mathbb C)$
negative_passages.docid: 13371
negative_passages.text: Show that the Lie algebra generated by x, y with relations $ad(x)^2(y) = ad(y)^5(x) = 0$ is infinite dimensional and construct a basis
negative_passages.docid: 128229
negative_passages.text: Proving that the transformation obtained from an adjoint pair is natural
negative_passages.docid: 96380
negative_passages.text: Representation of $\text{sl}(2,\mathbb{C})$