Galois theory and commutators

Algebra Universalis

Volumn 65, Issue 2, 2011, Pages 161-177

  Everaert, Tomas ^a   van der Linden, Tim ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

associator; categorical Galois theory; commutator; higher central extension; semi abelian category

Indexed keywords

EID: 79953179976     PISSN: 00025240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00012-011-0121-8     Document Type: Article

References (28)

1. Borceux, F., Bourn, D.: Mal'cev, Protomodular, Homological and Semi-Abelian Categories. Mathematics and its Applications, vol. 566. Kluwer (2004).
2. Borceux F., Clementino M. M.: Topological semi-abelian algebras. Adv. Math. 130, 425-453 (2005).
3. Borceux, F., Janelidze, G.: Galois Theories. Cambridge Studies in Advanced Mathematics, vol. 72. Cambridge University Press (2001).
4. Bourn, D.: Normalization equivalence, kernel equivalence and affine categories. In: Carboni, A., Pedicchio, M. C., Rosolini, G. (eds.) Category Theory, Proceedings Como 1990. Lecture Notes in Mathematics, vol. 1488, pp. 43-62. Springer (1991).
5. Bourn D., Gran M.: Central extensions in semi-abelian categories. J. Pure Appl. Algebra 175, 31-44 (2002).
6. Bourn D., Janelidze G.: Characterization of protomodular varieties of universal algebras. Theory Appl. Categ. 11, 143-147 (2003).
7. Everaert T.: Relative commutator theory in varieties of Ω-groups. J. Pure Appl. Algebra 210, 1-10 (2007).
8. Everaert T.: Higher central extensions and Hopf formulae. J. Algebra 324, 1771-1789 (2010).
9. Everaert T., Gran M.: On low-dimensional homology in categories. Homology, Homotopy and Appl. 9, 275-293 (2007).
10. Everaert T., Gran M.: Relative commutator associated with varieties of n-nilpotent and of n-solvable groups. Arch. Math. (Brno) 42, 387-396 (2007).
11. Everaert T., Gran M., van der Linden T.: Higher Hopf formulae for homology via Galois theory. Adv. Math. 217, 2231-2267 (2008).
12. Everaert T., van der Linden T.: Baer invariants in semi-abelian categories I: General theory. Theory Appl. Categ. 12, 1-33 (2004).
13. Everaert T., van der Linden T.: Baer invariants in semi-abelian categories II: Homology. Theory Appl. Categ. 12, 195-224 (2004).
14. Everaert T., van der Linden T.: A note on double central extensions in exact Mal'tsev categories. Cah. Topol. Géom. Differ. Catég. 51, 143-153 (2010).
15. Everaert, T., van der Linden, T.: Relative commutator theory in semi-abelian categories (2010, submitted).
16. Fröhlich A.: Baer-invariants of algebras. Trans. Amer. Math. Soc. 109, 221-244 (1963).
17. Furtado-Coelho J.: Homology and generalized Baer invariants. J. Algebra 40, 596-609 (1976).
18. Goedecke J., van der Linden T.: On satellites in semi-abelian categories: Homology without projectives. Math. Proc. Cambridge Philos. Soc. 147, 629-657 (2009).
19. Higgins P. J.: Groups with multiple operators. Proc. London Math. Soc. 6, 366-416 (1956).
20. Janelidze G.: Pure Galois theory in categories. J. Algebra 132, 270-286 (1990).
21. Janelidze, G.: What is a double central extension? (The question was asked by Ronald Brown.) Cah. Topol. Géom. Differ. Catég. 32, 191-201 (1991).
22. Janelidze G., Kelly G. M.: Galois theory and a general notion of central extension. J. Pure Appl. Algebra 97, 135-161 (1994).
23. Janelidze G, Márki L., Tholen W.: Semi-abelian categories. J. Pure Appl. Algebra 168, 367-386 (2002).
24. Lavendhomme, R., Roisin, J. R. Cohomologie non abélienne de structures algébriques. J. Algebra 67: 385-414 (1980) (French).
25. Lue A. S.-T.: Baer-invariants and extensions relative to a variety. Math. Proc. Cambridge Philos. Soc. 63, 569-578 (1967).
26. Rodelo D., van der Linden T.: The third cohomology group classifies double central extensions. Theory Appl. Categ. 23, 150-169 (2010).
27. Ursini, A. Osservazioni sulle varietá BIT. Boll. Unione Mat. Ital. 4: 205-211 (1973) (Italian).
28. Ursini A.: On subtractive varieties I. Algebra Universalis 31, 204-222 (1994).