Abstract
In this paper, we define and investigate the notions of L-solvable radical and nilpotent radical for several kinds of triple systems, for example, δ -Jordan-Lie triple systems, Jordan triple systems, and Freudenthal-Kantor triple systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V.T. Filippov, n-Lie algebras, Sib. Math. Sh. 26(1985) 126–140.
N. Jacobson, Lie and Jordan triple systems, Amer. J. Math. 71(1947) 149–170.
N. Kamiya, On the Jacobson radicals and some radicals of Lie algebras, Research Reports of General Ed. Fac. Eng. Toyo Univ. 27(1982) 15–17.
N. Kamiya, A structure theory of Freudenthal-Kantor triple systems, J.Alg. 110(1987) 108–123.
N. Kamiya, A construction of anti-Lie triple systems from a class of triple systems, Mem.Fac.Sci. Shimane Univ. 22(1988) 51–62.
N. Kamiya, A structure theory of Freudenthal-Kantor triple systems II, Comm.Maht. Univ. St.Pauli, 38(1989) 41–62.
N. Kamiya, The construction of all simple Lie algebras over C from balanced Freudenthal-Kantor triple systems, Contributions to General Algebra 7, Verlag H’older-Picher-Tempsky, Wien, Verlag. G. Teubner, Stuttgart (1991) 205–213
N. Kamiya, Remarks on nil radical for Freudenthal-Kantor triple systems, Proc. 10th summer Seminar on Lie algebras, Hiroshima Univ. (1994) 24–27.
N. Kamiya, On Freudenthal-Kantor triple systems and generalized structurable algebras, Nonassociative algebras and its applications, Kluwer Acad.Pub. Math and its App. 303(1994) 198–203.
N. Kamiya, On the Peirce decompositions for Freudenthal-Kantor triple systems, Comm. in Alg. 25(1997) 1833–1844.
N. Kamiya, On a realization of the exceptional simple graded Lie algebras of second kind and Freudenthal-Kantor triple systems, Bull.Polish Acad. Sci.Math. 46(1998) 55–65.
N. Kamiya and S. Okubo, On classical Yang-Baxter equations associated with Freudenthal-Kantor triple systems, Advanced in Applied Clifford Algebras, 8(1998) 403–416, Mexico.
N. Kamiya, The Wedderburn Principal theorem, Nilpotency and Solvability for Freudenthal-Kantor triple systems, Matematica comtemporanea, (1999)129–136, Brazil.
N. Kamiya and S. Okubo, A construction of Jordan superalgebras from Jordan-Lie triple systems, (ed Costa), Lecture Note in Pure and App. Math. 211(2000) 171–176, Marcel Dekker Inc.
N. Kamiya and S. Okubo, On δ-Lie super triple systems associated with (ε, δ)-Freudenthal-Kantor supertriple systems, Proc. Edinburgh Math., Soc. 43(2000) 243–260.
N. Kamiya, Examples of Peirce decomposition associated with simple generalized Jordan triple systems of second order, preprint.
W.G. Lister, A structure theory of Lie triple systems, Trans. Amer. Math. Sic., 72(1952) 217–242.
S. Okubo, Introduction to octonion and other non-associative algebras in physics, Cambridge Univ. Press. (Cambridge/New York)1995.
S. Okubo and N. Kamiya, Jordan-Lie algebras and Jordan-Lie triple systems, J.Alg.198(1997)388–411.
M. Racine and E. Zelmanov, Simple Jordan superalgebras, Nonassociative algebras and its applications, Kluwer Acad.Pub.Math. and its App. 303(1994) 344–349.
E. Zelmanov and I.P. Shestakov, Prime alternative superalgebras and the nilpotency of the radical of a free alternative algebras, Math.USSR Izvestiya 37(1991) 19–36.
K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov, and A.I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, 104, Academic Press, New York, 1987
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Kluwer Academic Publishers
About this chapter
Cite this chapter
Kamiya, N. (2003). On Radicals of Triple Systems. In: Bahturin, Y. (eds) Groups, Rings, Lie and Hopf Algebras. Mathematics and Its Applications, vol 555. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0235-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0235-3_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7954-6
Online ISBN: 978-1-4613-0235-3
eBook Packages: Springer Book Archive