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Results tagged with lie-algebras
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user 36972
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.
9
votes
Accepted
Injectivity of Rewrite Rule in a Free Lie Algebra
Yes. Embed the free Lie algebra in the free associative algebra, then consider the monomial with $x_n$ as far right as possible (i.e., with the largest number of other $\{x_i,i\leq n\}$ before it): i …
- 630
3
votes
0
answers
422
views
Decomposition of a representation of SU(N) into representations of SU(N-1)
Let $\omega_k$ be the highest weight of the $k$-th antisymmetric representation of $\mathfrak{su}(N)$. Consider an irreducible representation of $\mathfrak{su}(N)$, characterized by its highest weigh …
- 630
6
votes
2
answers
188
views
Counting adjoints in the symmetric or antisymmetric square of a Lie group representation
EDIT (November 1, 2022): Over the weekend I think I found a technique to determine the exact multiplicities, according to how conjugation acts on the fundamental weights. While I haven't done the pre …
- 630