Project/Area Number |
09640078
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year 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)
|
Co-Investigator(Kenkyū-buntansha) |
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.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.
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