|Budget Amount *help
¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)
I.L. Kantor defined a generalized Jordan triple system (GJTS), and he constructed a graded Lie algebra (GLA) from it. The classification of real simple compact GJTS's of the 2nd order was given by S.Kaneyuki-H.Asano in case that the associated GLA's were classical. H.Asano tried to clasify non-compact real simple GJTS's of the 2nd order by a procedure to use the *-modification. He succeeded in classifying them in case that their GLA's were classical. On the other hand, K.Yamaguti defined a U(epsilon)-algebra (epsilon = *1)unifying a GJTS and a Freudenthal triple system (FTS). Our main purpose of this research was to classify GJTS's in case that the associated GLA's were exceptional. For this purpose, we extended Yamaguti's U(epsilon)-algebra to the case that epsilon was an automorphism of the triple system. In this research, we gave a general theory parallel to Asano's one, which is basic for carring out the classification of U(epsilon)-algebras (epsilon=*1). In the sequel, the classification of GJTS's and that of FTS's were completed simultaneously.
 H.Asano,Classification of non-compact real simple generalized Jordan triple systems of the second kind,Hiroshima Math.J.,21(1991),463-489.
 S.Kaneyuki and H.Asano,Graded Lie algebras and generalized Jordan triple systems,Nagoya Math.J.,112(1988),81-115.
 K.Yamaguti,On the metasymplectic geometry and triple systems,Kokyuroku RIMS,Kyoto Univ.308(1977),55-92(in Japanese).