Derivations of a Restricted Weyl-Type Algebra Containing the Polynomial Ring

摘要

A Weyl type nonassociative algebra and its subalgebra have been defined in the articles Choi and Nam (2005a2. Choi , S. H. , Nam , K.-B. ( 2005a ). The derivation of a restricted weyl type non-associative algebra . Hadronic Journal . Vol. 28 , Hadronic Press , pp. 287 - 295 .View all references b3. Choi , S. H. , Nam , K.-B. ( 2005b ). Derivations of symmetric non-associative algebra I . Algebras, Groups, and Geometries 22 ( 3 ): 341 - 352 .View all references c4. Choi , S. H. , Nam , K.-B. (2005c). Derivations of a restricted Weyl type algebra I. Rocky Mountain Journal of Mathematics 37(6):1813-1930.[CrossRef], [Web of Science ®]View all references); Lee and Nam (200411. Lee , K.-S. , Nam , K.-B. ( 2004 ). Some W-type algebras I . J. Appl. Algebra Discrete Struct. 2 ( 1 ): 39 - 46 .View all references). Several authors have found all the derivations of some given algebra (see Ahmadi et al., 20051. Ahmadi , M. H. , Nam , K.-B. , Pakinathan , J. ( 2005 ). Lie admissible non-associative algebras . Algebra Colloquium . Vol. 12 , No. 1 , World Scientific , pp. 113 - 120 .[Web of Science ®]View all references; Choi and Nam, 2005b3. Choi , S. H. , Nam , K.-B. ( 2005b ). Derivations of symmetric non-associative algebra I . Algebras, Groups, and Geometries 22 ( 3 ): 341 - 352 .View all references; Kac, 19747. Kac , V. G. ( 1974 ). Description of filtered Lie algebra with which Graded Lie algebras of Cartan type are associated . Izv. Akad. Nauk SSSR, Ser. Mat. Tom 38 : 832 - 834 .View all references; Kirkman et al., 19949. Kirkman , E. , Procesi , C. , Small , L. ( 1994 ). A q-analog for the Virasoro algebra . Comm. Algebra 22 ( 10 ): 3755 - 3774 .[Taylor & Francis Online], [Web of Science ®]View all references; Osborn, 199715. Osborn , J. M. ( 1997 ). Derivations and Isomorphisms of Lie Algebras of Characteristic 0 . Modular Interfaces (Riverside, CA, 1995), 95-108, AMS/IP Stud. Adv. Math., 4, Amer. Math. Soc., Providence, RI .View all references; Osborn and Passman, 199516. Osborn , J. M. , Passman , D. S. ( 1995 ). Derivations of skew polynomial rings . J. Algebra 176 ( 2 ): 417 - 448 .[CrossRef], [Web of Science ®]View all references). In this article, we find all derivations of the nonassociative algebra and show that the dimension of all derivations of the algebra is (s ₁ + s ₂)2 + s ₁ + s ₂. Because of the dimension of a derivation algebra, we know that if s ₁ + s ₂ ≠ s ₁′ + s ₂′, then the algebras and are not isomorphic.View full textDownload full textKey WordsAnnihilator, Derivation, Idempotent, Kronecker delta, Non-associative algebra, Right identity, Simple2000 Mathematics Subject ClassificationPrimary 17B40, 17B56Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870802107835