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Without any restriction on the length of <jats:italic>X<\/jats:italic>, we find only a sufficient condition involving certain equivalence relation on the set of maximal chains of <jats:italic>X<\/jats:italic>. For some classes of posets of length one, such as finite connected crownless posets (i.e., without weak crown subposets), crowns, and ordinal sums of two anti-chains, we give a complete answer.<\/jats:p>","DOI":"10.1017\/s0017089522000015","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T08:13:25Z","timestamp":1644221605000},"page":"702-715","source":"Crossref","is-referenced-by-count":3,"title":["Proper Lie automorphisms of incidence algebras"],"prefix":"10.1017","volume":"64","author":[{"given":"\u00c9rica Z.","family":"Fornaroli","sequence":"first","affiliation":[]},{"given":"Mykola","family":"Khrypchenko","sequence":"additional","affiliation":[]},{"suffix":"Jr.","given":"Ednei A.","family":"Santulo","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,2,7]]},"reference":[{"key":"S0017089522000015_ref22","volume-title":"Incidence Algebras","author":"Spiegel","year":"1997"},{"key":"S0017089522000015_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089515000166"},{"key":"S0017089522000015_ref18","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-44.1.213"},{"key":"S0017089522000015_ref16","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1963-0160798-4"},{"key":"S0017089522000015_ref11","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1130"},{"key":"S0017089522000015_ref9","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1329"},{"key":"S0017089522000015_ref8","unstructured":"[8] Cecil, A. 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