{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T23:39:02Z","timestamp":1648942742845},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:p> Let \ud835\udd3d be the underlying base field of characteristic p &lt; 3 and denote by [Formula: see text] and [Formula: see text] the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras [Formula: see text] and [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text] and [Formula: see text], we then determine the derivation algebra of [Formula: see text] and the derivation space of [Formula: see text] to [Formula: see text], where [Formula: see text] is viewed as a [Formula: see text]-module by means of the adjoint representation. As a result, we describe explicitly the derivation algebra of [Formula: see text]. Furthermore, we prove that the outer derivation algebras of [Formula: see text] and [Formula: see text] are abelian Lie algebras or metabelian Lie algebras with explicit structure. In particular, we give the dimension formulas of the derivation algebras and outer derivation algebras of [Formula: see text] and [Formula: see text]. Thus, we may make a comparison between the even parts of the (outer) superderivation algebras of W and S and the (outer) derivation algebras of the even parts of W and S, respectively. <\/jats:p>","DOI":"10.1142\/s0218196707003883","type":"journal-article","created":{"date-parts":[[2007,7,5]],"date-time":"2007-07-05T09:38:16Z","timestamp":1183628296000},"page":"661-714","source":"Crossref","is-referenced-by-count":10,"title":["DERIVATIONS OF THE EVEN PARTS FOR MODULAR LIE SUPERALGEBRAS OF CARTAN TYPE W AND S"],"prefix":"10.1142","volume":"17","author":[{"given":"WENDE","family":"LIU","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YONGZHENG","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/1971340"},{"key":"rf2","first-page":"126","volume":"98","author":"Celousov M. 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