An Extension of Raïs’ Theorem and Seaweed Subalgebras of Simple Lie Algebras
نویسنده
چکیده
If q is an algebraic Lie algebra and Q is an algebraic group with Lie algebra q, then ind q equals the transcendence degree of the field of Q-invariant rational functions on q. If q is reductive, then q and q are isomorphic as q-modules and hence ind q = rk q. It is an important invariant-theoretic problem to study index and, more generally, the coadjoint representation for non-reductive Lie algebras.
منابع مشابه
Fiber bundles and Lie algebras of top spaces
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
متن کاملClassification of Lie Subalgebras up to an Inner Automorphism
In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...
متن کاملInductive Formulas for the Index of Seaweed Lie Algebras
A seaweed subalgebra of a semisimple Lie algebra g is a generalization of the notion of parabolic subalgebra. In the case g = sl(V ), seaweed subalgebras were recently introduced by Dergachev and Kirillov. We give an inductive procedure for computing the index of seaweed subalgebras of classical Lie algebras. This allows us to prove that the index of any seaweed in sl(V ) or sp(V ) is at most t...
متن کاملOn permutably complemented subalgebras of finite dimensional Lie algebras
Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...
متن کاملPrimitive Subalgebras of Exceptional Lie Algebras
The object of this paper is to classify (up to inner automorphism) the primitive, maximal rank, reductive subalgebras of the (complex) exceptional Lie algebras. By primitive we mean that the subalgebras correspond to (possibly disconnected) maximal Lie subgroups. In [3], the corresponding classification for the (complex) classical Lie algebras was completed, as was the classification for the no...
متن کامل