Gradings induced by nilpotent elements
dc.contributor.author | García, Esther | |
dc.contributor.author | Gómez Lozano, Miguel | |
dc.contributor.author | Muñoz Alcázar, Rubén | |
dc.contributor.author | Vera de Salas, Guillermo | |
dc.date.accessioned | 2023-09-22T07:47:31Z | |
dc.date.available | 2023-09-22T07:47:31Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | 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 | es |
dc.identifier.issn | 0024-3795 | |
dc.identifier.uri | https://hdl.handle.net/10115/24475 | |
dc.description | The authors express their sincere thanks to the anonymous expert referee for the careful reading of the manuscript and his/her competent and insightful comments and suggestions. | es |
dc.description.abstract | 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 Φgrading 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. | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | von Neumann regular | es |
dc.subject | Nilpotent element | es |
dc.subject | Grading | es |
dc.subject | sl2-triple | es |
dc.title | Gradings induced by nilpotent elements | es |
dc.type | info:eu-repo/semantics/article | es |
dc.identifier.doi | 10.1016/j.laa.2022.09.017 | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
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