Nilpotency degree of the nilradical of a solvable Lie algebra on two generators and uniserial modules associated to free nilpotent Lie algebras
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 nilpot...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/143320 |
| Acceso en línea: | http://hdl.handle.net/11336/143320 |
| Access Level: | acceso abierto |
| Palabra clave: | FREE ℓ-STEP NILPOTENT LIE ALGEBRA INDECOMPOSABLE NILPOTENCY CLASS UNISERIAL https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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. |
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