Let K be a field and X a connected partially ordered set. In this talk, 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 present a characterization of the involutions of the second kind on FI(X,K). We conclude by giving necessary and sufficient conditions for two involutions of the second kind on FI(X,K) to be equivalent in the case where the characteristic of K is different from 2 and every multiplicative automorphism of FI(X,K) is inner.
This video is part of the European Non-Associative Algebra Seminar series.
