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2015 | 13 | 1 |
Tytuł artykułu

Restricted and quasi-toral restricted Lie-Rinehart algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-02-04
zaakceptowano
2015-08-20
online
2015-09-25
Twórcy
autor
  • School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China
  • School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China, chenly640@nenu.edu.cn
Bibliografia
  • [1] J. Casas, Obstructions to Lie-Rinehart Algebra Extensions. Algebra Colloq. 18 (2011), 83-104.[WoS]
  • [2] J. Casas, M. Ladra, T. Pirashvili, Crossed modules for Lie-Rinehart algebras. J. Algebra 274 (2004), 192-201.[WoS]
  • [3] L. Chen, D. Meng, B. Ren, On quasi-toral restricted Lie algebras. Chinese Ann. Math. Ser B 26 (2005), 207-218.[Crossref]
  • [4] B. Chew, On the commutativity of restricted Lie algebras. Proc. Amer. Math. Soc. 16 (1965), 547.
  • [5] Z. Chen, Z. Liu, D. Zhong, Lie-Rinehart bialgebras for crossed products. J. Pure Appl. Algebra 215 (2011), 1270-1283.[WoS]
  • [6] I. Dokas, Cohomology of restricted Lie-Rinehart algebras and the Brauer group. Adv. Math. 231 (2012), 2573-2592.[WoS]
  • [7] I. Dokas, J. Loday, On restricted Leibniz algebras. Comm. Algebra 34 (2006), 4467-4478.
  • [8] R. Farnsteiner, Conditions for the commutativity of restricted Lie algebras. Heidelberg and New York, 1967.
  • [9] R. Farnsteiner, Note on Frobenius extensions and restricted Lie superalgebras. J. Pure Appl. Algebra 108 (1996), 241-256.
  • [10] R. Farnsteiner, Restricted Lie algebras with semilinear p-mapping. Amer. Math. Soc. 91 (1984), 41-45.
  • [11] J. Herz, Pseudo-alg J ebras de Lie. C. R. Acad. Sci. paris 236 (1953), 1935-1937.
  • [12] T. Hodge, Lie triple system, restricted Lie triple system and algebraic groups. J. Algebra 244 (2001), 533-580.
  • [13] J. Huebschmann, Poisson cohomology and quantization. J. Reine Angew. Math. 408 (1990), 57-113.
  • [14] N. Jacobson, Lie algebras. Dover., Publ. New York, 1979.
  • [15] R. Palais, The cohomology of Lie rings. Amer. Math. Soc., Providence, R. I., Proc. Symp. Pure Math. (1961), 130-137.[Crossref]
  • [16] G. Rinehart, Differential forms on general commutative algebras. Trans. Amer. Math. Soc. 108 (1963), 195-222.
  • [17] H. Strade, R. Farnsteiner, Modular Lie algebras and their representations. New York: Marcel Dekker Inc. 300 (1988).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0049
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