RT Journal Article
T1 Gradings induced by nilpotent elements.
A1 García González, Esther
A1 Gómez-Lozano, Miguel Ángel
A1 Muñoz-Alcázar, Rubén José
A1 Vera de Salas, Guillermo
K1 Anillos (Álgebra)
K1 Anillos graduados
AB An element a is nilpotent last-regular if it is nilpotent and its last nonzero power is von Neumann regular. In this paper we show that any nilpotent last-regular element a in an associative algebra R over a ring of scalars Φ gives rise to a complete system of orthogonal idempotents that induces a finite Z-grading on R; we also show that such element gives rise to an sl2-triple in R with semisimple adjoint map adh, and that the grading of R with respect to the complete system of orthogonal idempotents is a refinement of the Φ grading induced by the eigenspaces of adh. These results can be adapted to nilpotent elements a with all their powers von Neumann regular, in which case the element a can be completed to an sl2-triple and a is homogeneous of degree 2 both in the Z-grading of R and in the Φ-grading given by the eigenspaces of adh.
PB Elsevier
YR 2023
FD 2023
LK https://hdl.handle.net/10630/27996
UL https://hdl.handle.net/10630/27996
LA eng
NO Esther García, Miguel Gómez Lozano, Rubén Muñoz Alcázar, Guillermo Vera de Salas, Gradings induced by nilpotent elements, Linear Algebra and its Applications, Volume 656, 2023, Pages 92-111, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2022.09.017
NO All authors were partially supported by the Junta de Andalucía FQM264 and by Universidad de Málaga, B4: Ayudas para Proyectos Puente UMA “Sistemas de Jordan, Álgebras de Lie y estructuras relacionadas”
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026