{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T07:14:11Z","timestamp":1648624451625},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> In this paper we study group actions on hyperbolic \u039b-metric spaces, where \u039b is an ordered abelian group. \u039b-metric spaces were first introduced by Morgan and Shalen in their study of hyperbolic structures and then Chiswell, following Gromov's ideas, introduced the notion of hyperbolicity for such spaces. Only the case of 0-hyperbolic \u039b-metric spaces (that is, \u039b-trees) was systematically studied, while the theory of general hyperbolic \u039b-metric spaces was not developed at all. Hence, one of the goals of the present paper was to fill this gap and translate basic notions and results from the theory of group actions on hyperbolic (in the usual sense) spaces to the case of \u039b-metric spaces for an arbitrary \u039b. The other goal was to show some principal difficulties which arise in this generalization and the ways to deal with them. <\/jats:p>","DOI":"10.1142\/s0218196715500289","type":"journal-article","created":{"date-parts":[[2015,7,20]],"date-time":"2015-07-20T23:29:08Z","timestamp":1437434948000},"page":"977-1042","source":"Crossref","is-referenced-by-count":1,"title":["Groups acting on hyperbolic \u039b-metric spaces"],"prefix":"10.1142","volume":"25","author":[{"given":"Andrei-Paul","family":"Grecianu","sequence":"first","affiliation":[{"name":"Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA"}]},{"given":"Alexei V.","family":"Kvaschuk","sequence":"additional","affiliation":[{"name":"Bank of America Corporate Center, 100 N Tryon St, Charlotte, North Carolina 28255, USA"}]},{"given":"Alexei G.","family":"Myasnikov","sequence":"additional","affiliation":[{"name":"Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA"}]},{"given":"Denis E.","family":"Serbin","sequence":"additional","affiliation":[{"name":"Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA"}]}],"member":"219","published-online":{"date-parts":[[2015,9,29]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","unstructured":"R.\u00a0Alperin and H.\u00a0Bass, Combinatorial Group Theory and Topology, Annals of Mathematics Studies\u00a0111, eds. 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