1988 Fiscal Year Final Research Report Summary
Study on the structure of generalized Lie triple systems.
| Project/Area Number |
62540050
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
YAMAGUCHI Kiyosi Fac. of School Education, Hiroshima University, Prof., 学校教育学部, 教授 (20040090)
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| Co-Investigator(Kenkyū-buntansha) |
IKEDA Akira Fac. of School Education, Hiroshima University, Prof., 教校教育学部, 助教授 (30093363)
KAGEYAMA Sanpei Fac. of School Education, Hiroshima University, Prof., 学校教育学部, 助教授 (70033892)
ISHIBASHI Yasunori Fac. of School Education, Hiroshima University, Prof., 学校教育学部, 教授 (30033848)
SHINTANI Naoyoshi Fac. of School Education, Hiroshima University, Prof., 学校教育学部, 教授 (90033802)
NASU Toshio Fac. of Education, Hiroshima University, Prof., 教育学部, 教授 (90033026)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Generalized Lie triple system / Generalized J-ternary system / Freudenthal-Kantor pair / Lie algebra / Lie superalgebra / 結合的三項系 |
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| Research Abstract |
A generalized lie triple system(GLTS) is an algebraic system with a bilinear alternative product and a trilinear product satisfying some conditions. GLTS is the tangent algebra at eh of the reductive homogeneous space G/H and GLTS is a generalization of a Lie algebra and a Lie triple system. We reneralize the notion of GLTS as the quadruple of lie algebra L, a certain algebraic system B with bilinear and trilinear product, a special representation of lie algebra L into B, and a certain bilinear mapping of B into L, then it is shown that a lie algebra is constructed from this quadruple. Some examples of GLTS are constructed.
From a commutative associative triple pair and a generalized J-(super) ternary pair, by considering their tensor product, a new generalized J-(super) ternary pair is obtaines( with H. Tanabe ).
For two commutative associative triple systems A_1, A_2 and a Freudenthal-kantor (super) triple system U (- , ), = 1, the tensor product A_1 U(- , ) A_2 becomes a Lie triple system or anti-Lie triple system, hence the Lie algebra and lie superalgebra are obtained as the imbedding lie (super)algebra according to =1 and -1. The tripleness in the mathematics education was also studied.
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