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Algebra Comput."],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:p> We prove that every derivation and every locally nilpotent derivation of the subalgebra [Formula: see text], where [Formula: see text], of the polynomial algebra [Formula: see text] in two variables over a field [Formula: see text] of characteristic zero is induced by a derivation and a locally nilpotent derivation of [Formula: see text], respectively. Moreover, we prove that every automorphism of [Formula: see text] over an algebraically closed field [Formula: see text] of characteristic zero is induced by an automorphism of [Formula: see text]. We also show that the group of automorphisms of [Formula: see text] admits an amalgamated free product structure. <\/jats:p>","DOI":"10.1142\/s0218196723500182","type":"journal-article","created":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T13:06:41Z","timestamp":1677244001000},"page":"351-367","source":"Crossref","is-referenced-by-count":3,"title":["Automorphisms of affine Veronese surfaces"],"prefix":"10.1142","volume":"33","author":[{"given":"Bakhyt","family":"Aitzhanova","sequence":"first","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, MI 48202, USA"}]},{"given":"Ualbai","family":"Umirbaev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, MI 48202, USA"},{"name":"Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan"}]}],"member":"219","published-online":{"date-parts":[[2023,3,29]]},"reference":[{"key":"S0218196723500182BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/9789814436700_0001"},{"key":"S0218196723500182BIB003","series-title":"New Mathematical Monographs","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511542794","volume-title":"Free Ideal Rings and Localization in General Rings","volume":"3","author":"Cohn P. 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