{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T05:11:04Z","timestamp":1772082664197,"version":"3.50.1"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> We study post-Lie algebra structures on [Formula: see text] for nilpotent Lie algebras. First, we show that if [Formula: see text] is nilpotent such that [Formula: see text], then also [Formula: see text] must be nilpotent, of bounded class. For post-Lie algebra structures [Formula: see text] on pairs of [Formula: see text]-step nilpotent Lie algebras [Formula: see text] we give necessary and sufficient conditions such that [Formula: see text] defines a CPA-structure on [Formula: see text], or on [Formula: see text]. As a corollary, we obtain that every LR-structure on a Heisenberg Lie algebra of dimension [Formula: see text] is complete. Finally, we classify all post-Lie algebra structures on [Formula: see text] for [Formula: see text], where [Formula: see text] is the three-dimensional Heisenberg Lie algebra. <\/jats:p>","DOI":"10.1142\/s0218196718500406","type":"journal-article","created":{"date-parts":[[2018,5,28]],"date-time":"2018-05-28T03:36:42Z","timestamp":1527478602000},"page":"915-933","source":"Crossref","is-referenced-by-count":4,"title":["Post-Lie algebra structures for nilpotent Lie algebras"],"prefix":"10.1142","volume":"28","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":"Christof","family":"Ender","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria"}]},{"given":"Wolfgang Alexander","family":"Moens","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":[[2018,8,17]]},"reference":[{"issue":"2","key":"S0218196718500406BIB001","first-page":"17","volume":"55","author":"Bai C.","year":"2014","journal-title":"J. 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