info:eu-repo/semantics/article
Nilpotency degree of the nilradical of a solvable Lie algebra on two generators and uniserial modules associated to free nilpotent Lie algebras
Fecha
2021-11-20Registro en:
Cagliero, Leandro Roberto; Levstein, Fernando; Szechtman, Fernando; Nilpotency degree of the nilradical of a solvable Lie algebra on two generators and uniserial modules associated to free nilpotent Lie algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 585; 20-11-2021; 447-483
0021-8693
CONICET Digital
CONICET
Autor
Cagliero, Leandro Roberto
Levstein, Fernando
Szechtman, Fernando
Resumen
Given a sequence d~ = (d1, . . . , dk) of natural numbers, we consider
the Lie subalgebra h of gl(d, F), where d = d1 + · · · + dk and F is a field of
characteristic 0, generated by two block upper triangular matrices D and E
partitioned according to d~, and study the problem of computing the nilpotency
degree m of the nilradical n of h. We obtain a complete answer when D and E
belong to a certain family of matrices that arises naturally when attempting
to classify the indecomposable modules of certain solvable Lie algebras.
Our determination of m depends in an essential manner on the symmetry of
E with respect to an outer automorphism of sl(d). The proof that m depends
solely on this symmetry is long and delicate.
As a direct application of our investigations on h and n we give a full
classification of all uniserial modules of an extension of the free ℓ-step nilpotent
Lie algebra on n generators when F is algebraically closed.