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ON SOLVABILITY AND NILPOTENCY OF ALGEBRAS WITH BRACKET

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We analyze properties of solvable and nilpotent algebras with bracket. The class of solvability and nilpotency of the tensor square of an algebra with bracket is obtained. Homological characterizations of nilpotent algebras with bracket are presented.

Abstract

We analyze properties of solvable and nilpotent algebras with bracket. The class of solvability and nilpotency of the tensor square of an algebra with bracket is obtained. Homological characterizations of nilpotent algebras with bracket are presented.

참고문헌 (20)

  1. R. Baer, "Representations of groups as quotient groups. I", Trans. Amer. Math. Soc, 58, pp.295~347 (1945)
  2. R. Baer, "Representations of groups as quotient groups. II. Minimal central chains of a group", Trans. Amer. Math. Soc, 58, pp.348~389 (1945)
  3. R. Baer, "Representations of groups as quotient groups. III. Invariants of classes of re-lated representations", Trans. Amer. Math. Soc, 58, pp.390~419 (1945)
  4. F. Borceux, "Galois theory, Hopf algebras and semi-abelian categories", pp.27~60 (2004), Amer. Math. Soc
  5. F. Borceux, "Mal’cev, protomodular, homological and semi-abelian cate-gories" (2004), Kluwer Academic Publihers
  6. J. M. Casas, "Homology with trivial coefficients and universal central extensions of alge-bras with bracket", Comm. Algebra, 35(8), pp.2431~2449 (2007)
  7. J. M. Casas, "Non-commutative Leibniz-Poisson algebras", Comm. Algebra, 34(7), pp.2507~2530 (2006)
  8. J. M. Casas, "Left-Right noncommutative Poisson algebras", Cent. Eur. J. Math, 12(1), pp.57~78 (2014)
  9. J. M. Casas, "Algebras with bracket", Manuscripta Math, 119(1), pp.1~15 (2006)
  10. T. Everaert, "Baer invariants in semi-abelian categories. I. Gen-eral theory", Theory Appl. Categ, 12(1), pp.1~33 (2004)
  11. A. Frohlich, "Baer-invariants of algebras", Trans. Amer. Math. Soc, 109, pp.221~244 (1963)
  12. M. Gel’fand, "Hamiltonian operators and algebraic structures related to them", Funct. Anal. Appl, 13, pp.248~262 (1980)
  13. J. E. Humphreys, "Introduction to Lie Algebras and Representation Theory" (1972), Springer
  14. S. A. Huq, "Commutator, nilpotency, and solvability in categories", Quart. J. Math. Oxford Ser, 19, pp.363~389 (1968)
  15. N. Jacobson, "Lie algebras" (1962), Interscience Publishers, John Wiley & Sons
  16. I. V. Kanatchikov, "On field theoretic generalizations of a Poisson algebra", Rep. Math. Phys, 40(2), pp.225~234 (1997)
  17. C. R. Leedham-Green, "Baer-invariants, isologism, varietal laws and homology", Acta Math, 137(1-2), pp.99~150 (1976)
  18. J.-L. Loday, "Dialgebras and related operads" (2001), Springer
  19. F. I. Michael, "A note on the Five Lemma", Appl. Categ. Structures, 21(5), pp.441~448 (2013)
  20. I. S. Rakhimov, "Complete list of low dimensional complex associative algebras", arXiv 0910.0932, ~ (2009)

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