Invariant subspaces of nilpotent linear operators, I

By Claus Michael Ringel, Markus Schmidmeier. 2006

110 citations recorded by the source corpus.

Abstract 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 → V a linear operator with Tn = 0 for some n, and such that T(U) 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 suffcient 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 indecomposable 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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a7e32433a0923129b21fa376788996f7b3421e54

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In Algebra and Number Theory

  1. Apostolos Beligiannis
  2. D. Kussin
  3. H. Lenzing
  4. H. Meltzer
  5. Xiao-Wu Chen
  6. Chrysostomos Psaroudakis
  7. J. Št’ovíček
  8. Mark Hovey

In Discrete Mathematics and Combinatorics

  1. Apostolos Beligiannis

In Geometry and Topology

  1. D. Kussin
  2. H. Lenzing
  3. H. Meltzer
  4. Apostolos Beligiannis
  5. Xiao-Wu Chen
  6. Pu Zhang
  7. Chrysostomos Psaroudakis
  8. J. Št’ovíček

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