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Original Articles

Free generic Poisson fields and algebras

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Pages 1799-1812 | Received 29 Oct 2015, Published online: 07 Sep 2017

References

  • Arenas, M., Arenas-Cartona, L. (2013). Universal Poisson envelope for binary Lie algebras. Commun. Algebra 41(5):1781–1789.
  • Bergman, G. M. (1969). Centralizers in free associative algebras. Trans. Amer. Math. Soc. 137:327–344.
  • Cohn, P. M. (1964). Subalgebras of free associative algebras. Proc. London Math. Soc. 56:618–632.
  • Cohn, P. M. (2006). Free Ideal Rings and Localization in General Rings. New Mathematical Monographs, Vol. 3. Cambridge: Cambridge University Press.
  • Czerniakiewicz, A. J. (1971). Automorphisms of a free associative algebra of rank 2, I. Trans. Amer. Math. Soc. 160:393–401; II, Trans. Amer. Math. Soc. 171, 1972, 309–315.
  • Eilenberg, S. (1948). Extensions of algebras. Ann. Soc. Pol. Math. 21:125–134.
  • Jacobson, N. (1969). Structure and Representation of Jordan Algebras. Providence, R.I.: Amer. Math. Soc.
  • Jung, H. W. E. (1942). Uber ganze birationale Transformationen der Ebene. J. Reine Angew. Math. 184:161–174.
  • Kolesnikov, P., Makar-Limanov, L., Shestakov, I. (2014). The Freiheitssatz for Generic Poisson Algebras. Symmetry, Integrability and Geometry: Methods and Applications, Vol. 10, p. 1–15.
  • Makar-Limanov, L. (1970). The automorphisms of the free algebra with two generators. Funct. Anal. Appl. 4:262–263.
  • Makar-Limanov, L., Shestakov, I. (2012). Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields. J. Algebra 349:372–379.
  • Makar-Limanov, L., Turusbekova, U., Umirbaev, U. (2009). Automorphisms and derivations of free Poisson algebras in two variables. J. Algebra 322(9):3318–3330.
  • Makar-Limanov, L., Umirbaev, U. (2007). Centralizers in free Poisson algebras. Proc. Amer. Math. Soc. 135(7): 1969–1975.
  • Makar-Limanov, L., Umirbaev, U. Free Poisson Fields and Their Automorphisms, http://arxiv.org/abs/1202.4382
  • Makar-Limanov, L., Umirbaev, U. (2011). The Freiheitssatz for Poisson algebras. J. Algebra 328:495–503.
  • Oh, S.-Q. (1999). Poisson enveloping algebras. Commun. Algebra 27(5):2181–2186.
  • Oh, S.-Q., Park, C.-G., Shin, Y.-Y. (2002). A Poincare-Birkhoff-Witt theorem for Poisson enveloping algebras. Commun. Algebra 30(10):4867–4887.
  • Pérez-Izquierdo, J. M. (2005). An envelope for Bol algebras. J. Algebra 284(2):480–493.
  • Pérez-Izquierdo, J. M. (2007). Algebras, hyperalgebras, nonassociative bialgebras and loops. Adv. Math. 208(2): 834–876.
  • Pérez-Izquierdo, J. M., Shestakov, I. P. (2004). An envelope for Malcev algebras. J. Algebra 272(1):379–393.
  • Rentschler, R. (1968). Operations du groupe additif sur le plan. C. R. Acad. Sci. Paris 267:384–387.
  • Shestakov, I. P. (1993). Quantization of Poisson superalgebras and the specialty of Jordan superalgebras of Poisson type. Algebra Logic 32(5):309–317.
  • Shestakov, I. (1998). Speciality Problem for Malcev Algebras and Poisson Malcev Algebras, Nonassociative Algebra and Its Applications (São Paulo, 1998), Lecture Notes in Pure and Appl. Math., Vol. 211. New York: Dekker, pp. 365–371.
  • Shestakov, I., Umirbaev, U. (2004). Poisson brackets and two-generated subalgebras of rings of polynomials. J. Amer. Math. Soc. 17(1):181–196.
  • Shestakov, I., Umirbaev, U. (2004). The tame and the wild automorphisms of polynomial rings in three variables. J. Amer. Math. Soc. 17(1):197–227.
  • Shestakov, I., Zhukavets, N. (2006). The Malcev Poisson superalgebra of the free Malcev superalgebra on one odd generator. J. Algebra Appl. 5(4):521–535.
  • Shirshov, A. I. (1954). Subalgebras of free commutative and free anticommutative algebras. Mat. Sbornik N.S. 34(76):81–88 (Russian).
  • Shirshov, A. I. (2009). Selected works of A. I. Shirshov. In: Bokut, L., Latyshev, V., Shestakov, I., Zelmanov, E., eds. Contemporary Mathematicians. Basel: Birkhäuser Verlag, viii+242 pp.
  • Umirbaev, U. U. (1994). On Schreier varieties of algebras. Algebra Logic 33(3):180–193.
  • Umirbaev, U. (2012). Universal enveloping algebras and universal derivations of Poisson algebras. J. Algebra 354:77–94.
  • Vershinin, V. (2003). On Poisson-Malcev structures, Monodromy and differential equations (Moscow, 2001). Acta Appl. Math. 75(1–3):281–292.

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