Linear maps preserving products equal to vertices of a path algebra
-
Abderrahim Adrabi
,
Driss Bennis
Abstract
This paper studies bijective linear maps that preserve products equal to the vertices on path algebras over a field. These maps are fully characterized on path algebras associated with connected finite acyclic quivers.
Acknowledgements
The authors express their sincere gratitude to the referees for their substantial and insightful comments, which significantly helped us improve the final presentation of this article.
References
[1] L. Catalano, On maps characterized by action on equal products, J. Algebra 511 (2018), 148–154. 10.1016/j.jalgebra.2018.06.022Search in Google Scholar
[2] L. Catalano, On maps preserving products equal to a rank-one idempotent, Linear Multilinear Algebra 69 (2021), no. 4, 673–680. 10.1080/03081087.2019.1614518Search in Google Scholar
[3] L. Catalano and M. Chang-Lee, On maps preserving rank-one nilpotents, Linear Multilinear Algebra 69 (2021), no. 16, 3092–3098. 10.1080/03081087.2019.1707753Search in Google Scholar
[4] L. Catalano, S. Hsu and R. Kapalko, On maps preserving products of matrices, Linear Algebra Appl. 563 (2019), 193–206. 10.1016/j.laa.2018.10.029Search in Google Scholar
[5] L. Catalano and H. Julius, On maps preserving products equal to a diagonalizable matrix, Comm. Algebra 49 (2021), no. 10, 4334–4344. 10.1080/00927872.2021.1919133Search in Google Scholar
[6] L. Catalano and H. Julius, On maps preserving products equal to fixed elements, J. Algebra 575 (2021), 220–232. 10.1016/j.jalgebra.2021.02.014Search in Google Scholar
[7] M. A. Chebotar, W.-F. Ke, P.-H. Lee and L.-S. Shiao, On maps preserving products, Canad. Math. Bull. 48 (2005), no. 3, 355–369. 10.4153/CMB-2005-033-8Search in Google Scholar
[8] M. A. Chebotar, W.-F. Ke, P.-H. Lee and N.-C. Wong, Mappings preserving zero products, Studia Math. 155 (2003), no. 1, 77–94. 10.4064/sm155-1-6Search in Google Scholar
[9] J. J. Garcés and M. Khrypchenko, Linear maps preserving products equal to primitive idempotents of an incidence algebra, J. Algebra 612 (2022), 460–474. 10.1016/j.jalgebra.2022.09.002Search in Google Scholar
[10] J. J. Garcés and M. Khrypchenko, Potent preservers of incidence algebras, Linear Algebra Appl. 635 (2022), 171–200. 10.1016/j.laa.2021.11.020Search in Google Scholar
[11]
X. J. Guo and L. B. Li,
[12] G. E. Martin, Transformation Geometry, Undergrad. Texts Math., Springer, New York, 1982. 10.1007/978-1-4612-5680-9Search in Google Scholar
[13] R. Schiffler, Quiver Representations, CMS Books Math./Ouvrages Math. SMC, Springer, Cham, 2014. 10.1007/978-3-319-09204-1Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
