Bi-element representations of ternary groups

Communications in Algebra

Volumn 34, Issue 5, 2006, Pages 1651-1670

  Borowiec, Andrzej ^a   Dudek, Wiesław A ^b   Duplij, Steven ^c  

^a UNIVERSITY OF WROC AW   (Poland)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^c V N KARAZIN KHARKIV NATIONAL UNIVERSITY   (Ukraine)

Author keywords

Matrix representation; Ternary group

Indexed keywords

EID: 33646789826     PISSN: 00927872     EISSN: 15324125     Source Type: Journal    
DOI: 10.1080/00927870500542564     Document Type: Article

References (37)

1. Abe, E. (1980). Hopf Algebras. Cambridge: Cambridge Univ. Press.
2. Belousov, V. D. (1972). n-ary Quasigroups. Kishinev: Shtintsa.
3. Benz, W., Ghalieh, K. (1998). Groupoids associated with the ternary rings of a projective plane. J. Geom. 61:17-31.
4. Borowiec, A., Dudek, W., Duplij, S. (2001). Basic concepts of ternary Hopf algebras. J. Kharkov National University ser. Nuclei, Particles, and Fields 529:21-29.
5. Carlsson, R. (1976). Cohomology of associative triple systems. Proc. Amer. Math. Soc. 60:1-7.
6. -1c of a group. Bull. Amer. Math. Soc: 49:869-877.
7. Demidov, E. E. (1998). Quantum Groups. Moscow: Factorial.
8. Dörnte, W. (1929). Unterschungen über einen verallgemeinerten Gruppenbegriff. Math. Z. 29:1-19.
9. Dudek, W. A. (1980). Remarks on n-groups. Demonstratio Math. 13:165-181.
10. Dudek, W. A. (1993). Autodistributive n-groups. Annales Sci. Math. Polonae, Commentationes Math. 23:1-11.
11. Dudek, I., Dudek, W. A. (1981). On skew elements in n-groups. Demonstratio Math. 14:827-833.
12. Dudek, W. A., Michalski, J. (1982). On a generalization of Hosszú theorem. Demonstratio Math. 15:437-441.
13. Dudek, W. A., Michalski, J. (1984). On retract of polyadic groups. Demonstratio Math. 17:281-301.
14. Dudek, W. A., Głazek, K., Gleichgewicht, B. (1977). A note on the axioms of n-groups. In: Universal Algebra. Coll. Math. Soc. J. Bolyai. 29. Hungary: Esztergom, pp. 195-202.
15. Głazek, K., Gleichgewicht, B. (1977). Abelian n-groups. In Universal Algebra. Coll. Math. Soc. J. Bolyai. 29. Hungary: Esztergom, pp. 321-329.
16. Kapranov, M., Gelfand, I. M., Zelevinskii, A. (1994). Discriminants, Resultants and Multidimensional Determinants. Berlin: Birkhäuser.
17. Kasner, E. (1904). An extension of the group concept. Bull. Amer. Math. Soc. 10:290-291.
18. Kassel, C. (1995). Quantum Groups. New York: Springer-Verlag.
19. Kerner, R. (2000). Ternary algebraic structures and their applications in physics. Preprint, Paris: Univ. P. & M. Curie.
20. Kurosh, A. G. (1974). General Algebra. Lectures for the academic year 1969-1970. Moscow: Izdat. "Nauka".
21. Lawrence, R. (1992). Algebras and triangle relations. In: Mickelson, J., Pekonetti, O., eds. Topological Methods in Field Theory. Singapore: World Sci., pp. 429-447.
22. Lister, W. G. (1971). Ternary rings. Trans. Amer. Math. Soc. 154:37-55.
23. Li, F., Duplij, S. (2002). Weak Hopf algebras and singular solutions of quantum Yang-Baxter equation. Commun. Math. Phys. 225:191-217.
24. Michalski, J. (1979). On some functors from the category of n-groups. Bull. Acad. Polon. Sci. Ser. Sci. Math. 27:345-349.
25. Nikshych, D., Vainerman, L. (2002). Finite quantum groupoids and their applications. In New Directions in Hopf Algebras. Math. Sci. Res. Inst. Publ. Cambridge: Cambridge Univ. Press, pp. 211-262.
26. Pojidaev, A. P. (2003). Enveloping algebras of Filippov algebras. Commun. Algebra 31:883-900.
27. Post, E. L. (1940). Polyadic groups. Trans. Amer. Math. Soc. 48:208-350.
28. Rusakov, S. A. (1998). Some Applications of n-ary Group Theory. Minsk: Belaruskaya navuka.
29. Shnider, S., Sternberg, S. (1993). Quantum Groups. Boston: International Press.
30. Sokolov, E. I. (1976). On the theorem of Gluskin-Hosszú on Dörnte groups. Mat. Issled. 39:187-189.
31. Sokolov, N. P. (1972). Introduction to the Theory of Multidimensional Matrices. Kiev: Naukova Dumka.
32. Taniguchi, Y. (2002). On the extensions of FK-ternary algebras. Sci. Math. Japon 55:281-295.
33. Vainerman, L., Kerner, R. (1996). On special classes of n-algebras. J. Math. Phys. 37:2553-2565.
34. Wanke-Jakubowska, M. B., Wanke-Jerie, M. E. (1984). On representations of n-groups. Annales Sci. Math. Polonae, Commentationes Math. 24:335-341.
35. Zeković, B., Artamonov, V. A. (1992). n-group rings and their radicals. Abelevy Gruppy Moduli (Tomsk) 11:3-7.
36. Zeković, B., Artamonov, V. A. (1999). A connection between some properties of n-group rings and group rings. Math. Montisnigri 11:151-158.
37. Zeković. B., Artamonov, V. A. (2002). On two problems for n-group rings. Math. Montisnigri 15:79-85.