Abstract
Let K be a field and X a connected partially ordered set. In the first part of this paper, we show that the finitary incidence algebra FI(X, K) of X over K has an involution of the second kind if and only if X has an involution and K has an automorphism of order 2. We also give a characterization of the involutions of the second kind on FI(X, K). In the second part, we give necessary and sufficient conditions for two involutions of the second kind on FI(X, K) to be equivalent in the case where \({{\,\textrm{char}\,}}K\ne 2\) and every multiplicative automorphism of FI(X, K) is inner.
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Fornaroli, É.Z. Involutions of the Second Kind on Finitary Incidence Algebras. Bull Braz Math Soc, New Series 54, 53 (2023). https://doi.org/10.1007/s00574-023-00370-8
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DOI: https://doi.org/10.1007/s00574-023-00370-8