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Algebra Logika, 2007, Volume 46, Number 5, Pages 560–584 (Mi al315)  

This article is cited in 9 scientific papers (total in 9 papers)

The Chevalley and Costant theorems for Mal'tsev algebras

V. N. Zhelyabina, I. P. Shestakovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Universidade de São Paulo, Instituto de Matemática e Estatística

Abstract: Centers of universal envelopes for Mal'tsev algebras are explored. It is proved that the center of the universal envelope for a finite-dimensional semisimple Mal'tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module over its center. Centers of universal enveloping algebras are computed for some Mal'tsev algebras of small dimensions.

Keywords: Lie algebra, Mal'tsev algebra, bialgebra, universal enveloping algebra, primitive elements, center of algebra, Chevalley theorem, Costant theorem.

Full text: PDF file (259 kB)
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English version:
Algebra and Logic, 2007, 46:5, 303–317

Bibliographic databases:

UDC: 512.554
Received: 12.03.2007

Citation: V. N. Zhelyabin, I. P. Shestakov, “The Chevalley and Costant theorems for Mal'tsev algebras”, Algebra Logika, 46:5 (2007), 560–584; Algebra and Logic, 46:5 (2007), 303–317

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. P. Pozhidaev, “Dialgebras and related triple systems”, Siberian Math. J., 49:4 (2008), 696–708  mathnet  crossref  mathscinet  zmath  isi
    2. V. N. Zhelyabin, “Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras”, Siberian Math. J., 50:6 (2009), 1011–1026  mathnet  crossref  mathscinet  isi  elib  elib
    3. Bremner M.R., Hentzel I.R., Peresi L.A., Usefi H., “Universal Enveloping Algebras of the Four-Dimensional Malcev Algebra”, Algebras, Representations and Applications, Contemporary Mathematics Series, 483, 2009, 73–89  crossref  mathscinet  zmath  adsnasa  isi
    4. Tvalavadze M.V., Bremner M.R., “Enveloping Algebras of Solvable Malcev Algebras of Dimension Five”, Comm Algebra, 39:8 (2011), 2816–2837  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kharchenko V.K., Shestakov I.P., “Generalizations of Lie Algebras”, Adv. Appl. Clifford Algebr., 22:3, SI (2012), 721–743  crossref  mathscinet  zmath  isi  elib  scopus
    6. T. I. Shabalin, “The centralizer of a $3$-dimensional simple subalgebra in the universal enveloping algebra of a $7$-dimensional simple Malcev algebra”, Siberian Math. J., 54:4 (2013), 759–768  mathnet  crossref  mathscinet  isi
    7. Alonso Alvarez J.N., Fernandez Vilaboa J.M., Gonzalez Rodriguez R., Soneira Calvo C., “Cleft Comodules Over Hopf Quasigroups”, Commun. Contemp. Math., 17:6 (2015), 1550007  crossref  mathscinet  zmath  isi  scopus
    8. Perez-Izquierdo J.M., Shestakov I.P., “Co-Moufang Deformations of the Universal Enveloping Algebra of the Algebra of Traceless Octonions”, Algebr. Represent. Theory, 18:5 (2015), 1247–1265  crossref  mathscinet  zmath  isi  elib  scopus
    9. Alonso Alvarez J.N., Fernandez Vilaboa J.M., Gonzalez Rodriguez R., “Cleft Extensions For Quasi-Entwining Structures”, Math. Slovaca, 68:2 (2018), 339–352  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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