Invariant Subspaces of Nilpotent Linear Operators. I

Details Invariant Subspaces of Nilpotent Linear Operators. I Invariant Subspaces of Nilpotent Linear Operators. I

2006-08-28

arxiv.org/abs/math/0608666v2

Mathematics

Representation Theory

55 pages, minor modification in (0.1.3), to appear in: Journal fuer die reine und angewandte Mathematik

Scientific paper

Let $k$ be a field. We consider triples $(V,U,T)$, where $V$ is a finite dimensional $k$-space, $U$ a subspace of $V$ and $T \:V \to V$ a linear operator with $T^n = 0$ for some $n$, and such that $T(U) \subseteq U$. Thus, $T$ is a nilpotent operator on $V$, and $U$ is an invariant subspace with respect to $T$. We will discuss the question whether it is possible to classify these triples. These triples $(V,U,T)$ are the objects of a category with the Krull-Remak-Schmidt property, thus it will be sufficient to deal with indecomposable triples. Obviously, the classification problem depends on $n$, and it will turn out that the decisive case is $n=6.$ For $n < 6$, there are only finitely many isomorphism classes of indecomposables triples, whereas for $n > 6$ we deal with what is called ``wild'' representation type, so no complete classification can be expected. For $n=6$, we will exhibit a complete description of all the indecomposable triples.

Affiliated with

Also associated with

No associations

Rating

Invariant Subspaces of Nilpotent Linear Operators. I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariant Subspaces of Nilpotent Linear Operators. I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant Subspaces of Nilpotent Linear Operators. I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-106436