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Garcés, Jorge J.; Khrypchenko, Mykola
Linear algebra and its applications, 02/2022, Letnik: 635Journal Article
Let X be a finite connected poset, F a field and I(X,F) the incidence algebra of X over F. We describe the bijective linear idempotent preservers φ:I(X,F)→I(X,F). Namely, we prove that, whenever char(F)≠2, φ is either an automorphism or an anti-automorphism of I(X,F). If char(F)=2 and |F|>2, then φ is a (in general, non-proper) Lie automorphism of I(X,F). Finally, if F=Z2, then φ is the composition of a bijective shift map and a Lie automorphism of I(X,F). Under certain restrictions on the characteristic of F we also obtain descriptions of the bijective linear maps which preserve tripotents and, more generally, k-potents of I(X,F) for k≥3.
