Let
X
X
be a finite connected poset and
K
K
a field. We give a full description of the Lie automorphisms of the incidence algebra
I
(
X
,
K
)
I(X,K)
. In particular, we show that they are in general not proper.
Let X be a finite connected poset and K a field. We give a full description of Lie automorphisms of the incidence algebra I(X, K). In particular, we show that they are in general not proper.
Let I(X, R) be the incidence algebra of the preordered set X over the ring R. In the case of a finite connected partially ordered set X, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra I(X, R). As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms.
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