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.
Communicated by K. A. KearnesLet X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI(X), to be equivalent in the case when every multiplicative automorphism of FI(X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra 60 (2012) 181-188] for finitary incidence algebras.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.