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Results tagged with lie-algebras
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user 6753
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
10
votes
Lie algebras with abelian Cartan subalgebras
The subalgebra of diagonal matrices in the (non-reductive) standard Borel subalgebra ${\mathfrak b}$ of ${\mathfrak gl}_2$ is an abelian Cartan subalgebra of ${\mathfrak b}$, since it is abelian (henc …
- 3,183
14
votes
Accepted
Three-dimensional simple Lie algebras over the rationals
Let me flesh out my comments. First, why there are infinitely many three-dimensional simple Lie algebras over $\mathbb Q$. One of the major steps in proving class field theory is to prove that we have …
- 3,183
11
votes
Accepted
Infinite dimensional unitary representations of SU(2) for non-half-integer j?
I just wrote this answer on your last question. To summarize, you can't have an irreducible representation of a compact group that is infinite dimensional, unless the representation space is very exot …
- 3,183