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)

Research Abstract 
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.KaneyukiH.Asano in case that the associated GLA's were classical. H.Asano tried to clasify noncompact 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. [1] H.Asano,Classification of noncompact real simple generalized Jordan triple systems of the second kind,Hiroshima Math.J.,21(1991),463489. [2] S.Kaneyuki and H.Asano,Graded Lie algebras and generalized Jordan triple systems,Nagoya Math.J.,112(1988),81115. [3] K.Yamaguti,On the metasymplectic geometry and triple systems,Kokyuroku RIMS,Kyoto Univ.308(1977),5592(in Japanese).
