Regular Hom-Lie structures on incidence algebras

We fully characterize regular Hom-Lie structures on the incidence algebra I ( X ,  K ) of a finite connected poset X over a field K . We prove that such a structure is the sum of a central-valued linear map annihilating the Jacobson radical of I ( X ,  K ) with the composition of certain inner and m...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023-07, Vol.117 (3), Article 122
Main Authors: Fornaroli, Érica Z., Khrypchenko, Mykola, Santulo, Ednei A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Automorphisms
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Set theory
Theoretical
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Summary:We fully characterize regular Hom-Lie structures on the incidence algebra I ( X ,  K ) of a finite connected poset X over a field K . We prove that such a structure is the sum of a central-valued linear map annihilating the Jacobson radical of I ( X ,  K ) with the composition of certain inner and multiplicative automorphisms of I ( X ,  K ).
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01454-2