{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T05:11:09Z","timestamp":1772082669137,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"Austrian Science Foundation FWF","award":["I 3248"],"award-info":[{"award-number":["I 3248"]}]},{"name":"Austrian Science Foundation FWF","award":["P 33811"],"award-info":[{"award-number":["P 33811"]}]},{"name":"FWF","award":["P 33811"],"award-info":[{"award-number":["P 33811"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p> We study rigidity questions for pairs of Lie algebras [Formula: see text] admitting a post-Lie algebra structure. We show that if [Formula: see text] is semisimple and [Formula: see text] is arbitrary, then we have rigidity in the sense that [Formula: see text] and [Formula: see text] must be isomorphic. The proof uses a result on the decomposition of a Lie algebra [Formula: see text] as the direct vector space sum of two semisimple subalgebras. We show that [Formula: see text] must be semisimple and hence isomorphic to the direct Lie algebra sum [Formula: see text]. This solves some open existence questions for post-Lie algebra structures on pairs of Lie algebras [Formula: see text]. We prove additional existence results for pairs [Formula: see text], where [Formula: see text] is complete, and for pairs, where [Formula: see text] is reductive with [Formula: see text]-dimensional center and [Formula: see text] is solvable or nilpotent. <\/jats:p>","DOI":"10.1142\/s0218196722500679","type":"journal-article","created":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T15:52:33Z","timestamp":1662738753000},"page":"1495-1511","source":"Crossref","is-referenced-by-count":2,"title":["Rigidity results for Lie algebras admitting a post-Lie algebra structure"],"prefix":"10.1142","volume":"32","author":[{"given":"Dietrich","family":"Burde","sequence":"first","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria"}]},{"given":"Karel","family":"Dekimpe","sequence":"additional","affiliation":[{"name":"Katholieke Universiteit Leuven Kulak, E. Sabbelaan 53 Bus 7657, 8500 Kortrijk, Belgium"}]},{"given":"Mina","family":"Monadjem","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria"}]}],"member":"219","published-online":{"date-parts":[[2022,10,11]]},"reference":[{"key":"S0218196722500679BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02315-6"},{"issue":"3","key":"S0218196722500679BIB002","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1006\/jabr.1996.0151","volume":"181","author":"Burde D.","year":"1996","journal-title":"J. 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