JournalscmhVol. 79 , No. 2DOI 10.1007/s00014-003-0788-3

Varieties of pairs of nilpotent matrices annihilating each other

  • Jan Schröer

    University of Leeds, UK
Varieties of pairs of nilpotent matrices annihilating each other cover

Abstract

We classify the irreducible components of the varieties

\V(n,a,b)={(A,B)\Mn(\field)×\Mn(\field)AB=BA=Aa=Bb=0}.\V(n,a,b) = \{ (A,B) \in \M_n(\field) \times \M_n(\field) \mid AB = BA = A^a = B^b = 0 \}.