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Results tagged with lie-algebras
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user 136058
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.
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Property of a semisimple Lie algebra over complex number field
Is the following property true？
Let $L$ be a finite-dimensional Lie algebra over $\mathbb{C}$. Then $L$ is semisimple if and only if for every $x \in L$, there exists $y, z\in L$, such that $x=[y, z …
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Weight spaces of modules over Lie algebras [closed]
I know that an irreducible infinite-dimensional weight module over the Virasoro algebra in which it has a non-zero finite-dimensional weight space, then all its weight spaces have finite dimension. Do …
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References for representations of Heisenberg Lie algebra
"Finite and infinite dimensional Lie algebras and applications in Physics" by G.G.A. Bäuerle and E.A. de Kerf.
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Derivations of universal enveloping algebra of Lie algebras
We know a lot about derivations of Lie algebra. However, for the universal enveloping algebra of Lie algebra, we have few references about it.
My question: describing the derivations of enveloping …
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Embedding problems on quantum groups？
We work over the field of complex numbers.
We have known that Lie algebra of type $A_2 $is a subalgebra of type $G_2$. However, when we consider their quantum groups, is this true i.e. does there exi …
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