Project/Area Number  09640078 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Nishinippon Institute of Technology 
Principal Investigator 
TANIGUCHI Yoshiaki Nishinippon inst.Tech., Fac.Engi., Assist.Prof., 工学部, 助教授 (80125161)

CoInvestigator(Kenkyūbuntansha) 
ATSUYAMA K Kumamoto inst.Tech., Gen.Ed., Prof., 総合教育, 教授 (60099075)

Project Period (FY) 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

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)

Keywords  Jordan tride system / Lie triple system / Lie algebra / Graded Lie algebras / Jordan triple systems / Lie triple systems 
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.
