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oai:riuma.uma.es:10630/279962026-02-03T11:27:35Zcom_10630_2254col_10630_37953

Gradings induced by nilpotent elements. García González, Esther Gómez-Lozano, Miguel Ángel Muñoz-Alcázar, Rubén José Vera de Salas, Guillermo Anillos (Álgebra) Anillos graduados 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. 2023-11-10T12:24:27Z 2023-11-10T12:24:27Z 2023 2023 journal article 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 https://hdl.handle.net/10630/27996 10.1016/j.laa.2022.09.017 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier