Gradings induced by nilpotent elements
Fecha
2022
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Elsevier
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Resumen
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.
Descripción
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.
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Citación
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
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