Browse > Article
http://dx.doi.org/10.4134/JKMS.j160213

ON SOLVABILITY AND NILPOTENCY OF ALGEBRAS WITH BRACKET  

Casas, Jose Manuel (Departamento Matematica Aplicada I Universidade de Vigo)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 647-662 More about this Journal
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.
Keywords
algebra with bracket; solvable algebra with bracket; nilpotent algebra with bracket;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. M. Casas and T. Datuashvili, Non-commutative Leibniz-Poisson algebras, Comm. Algebra 34 (2006), no. 7, 2507-2530.   DOI
2 J. M. Casas, T. Datuashvili, and M. Ladra, Left-Right noncommutative Poisson algebras, Cent. Eur. J. Math. 12 (2014), no. 1, 57-78.
3 J. M. Casas and T. Pirashvili, Algebras with bracket, Manuscripta Math. 119 (2006), no. 1, 1-15.   DOI
4 T. Everaert and T. Van der Linden, Baer invariants in semi-abelian categories. I. General theory, Theory Appl. Categ. 12 (2004), no. 1, 1-33.
5 A. Frohlich, Baer-invariants of algebras, Trans. Amer. Math. Soc. 109 (1963), 221-244.   DOI
6 M. Gel'fand and I. Dorfman, Hamiltonian operators and algebraic structures related to them, Funct. Anal. Appl. 13 (1980), 248-262.   DOI
7 J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Math. 9, Springer, 1972.
8 S. A. Huq, Commutator, nilpotency, and solvability in categories, Quart. J. Math. Oxford Ser. 19 (1968), 363-389.   DOI
9 N. Jacobson, Lie algebras, Interscience Publishers, John Wiley & Sons, New York-London, 1962.
10 I. V. Kanatchikov, On field theoretic generalizations of a Poisson algebra, Rep. Math. Phys. 40 (1997), no. 2, 225-234.   DOI
11 C. R. Leedham-Green and S. McKay, Baer-invariants, isologism, varietal laws and homology, Acta Math. 137 (1976), no, 1-2, 99-150.   DOI
12 R. Baer, Representations of groups as quotient groups. III. Invariants of classes of related representations, Trans. Amer. Math. Soc. 58 (1945), 390-419.   DOI
13 J.-L. Loday, A. Frabetti, F. Chapoton, and F. Goichot, Dialgebras and related operads, Lect. Notes in Math. 1763, Springer, 2001.
14 F. I. Michael, A note on the Five Lemma, Appl. Categ. Structures 21 (2013), no. 5, 441-448.   DOI
15 I. S. Rakhimov, I. M. Rikhsiboev, and W. Basri, Complete list of low dimensional complex associative algebras, arXiv 0910.0932 (2009).
16 R. Baer, Representations of groups as quotient groups. I, Trans. Amer. Math. Soc. 58 (1945), 295-347.
17 R. Baer, Representations of groups as quotient groups. II. Minimal central chains of a group, Trans. Amer. Math. Soc. 58 (1945), 348-389.   DOI
18 F. Borceux, A survey of semi-abelian categories, in Galois theory, Hopf algebras and semi-abelian categories, 27-60, Fields Inst. Commun., 43, Amer. Math. Soc., Providence, RI, 2004.
19 F. Borceux and D. Bourn, Mal'cev, protomodular, homological and semi-abelian categories, Mathematics and its Applications vol. 566, Kluwer Academic Publihers, 2004.
20 J. M. Casas, Homology with trivial coefficients and universal central extensions of algebras with bracket, Comm. Algebra 35 (2007), no. 8, 2431-2449.   DOI