| 1. |
- Kamiya, Noriaki, et al.
(author)
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A characterization of $(-1,-1)$-Freudenthal-Kantor triple systems
- 2011
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In: Glasgow Mathematical Journal. - 0017-0895. ; 53:3, s. 727-738
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Journal article (peer-reviewed)abstract
- In this paper, we discuss a connection between $(−1,−1)$-Freudenthal–Kantor triple systems, anti-structurable algebras, quasi anti-flexible algebras and give examples of such structures. The paper provides the correspondence and characterization of a bilinear product corresponding a triple product.
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| 2. |
- Kamiya, Noriaki, et al.
(author)
-
A review on $\delta$-structurable algebras
- 2011
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In: Banach Center Publications. - : Institute of Mathematics, Polish Academy of Sciences. - 1730-6299 .- 0137-6934. ; 93, s. 59-67
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Conference paper (peer-reviewed)abstract
- In this paper we give a review on $\delta$-structurable algebras. A connection between Malcev algebras and a generalization of $\delta$-structurable algebras is also given.
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| 3. |
- Kamiya, Noriaki, et al.
(author)
-
A Structure Theory of (-1,-1)-Freudenthal Kantor Triple Systems
- 2010
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In: Bulletin of the Australian Mathematical Society. - 0004-9727. ; 81:1, s. 132-155
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Journal article (peer-reviewed)abstract
- In this paper we discuss the simplicity criteria of (-1, -1)-Freudenthal Kantor triple systems and give examples of such triple systems, from which we can construct some Lie superalgebras. We also show that we can associate a Jordan triple system to any (epsilon, delta)-Freudenthal Kantor triple system. Further, we introduce the notion of delta-structurable algebras and connect them to (-1, delta)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction.
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| 4. |
- Kamiya, Noriaki, et al.
(author)
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$(\epsilon,\delta)$-Freudenthal Kantor triple systems, $\delta$-structurable algebras and Lie superalgebras
- 2010
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In: Algebras, Groups and Geometries. - 0741-9937. ; 2:27, s. 191-206
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Journal article (peer-reviewed)abstract
- In this paper we discuss $(\epsilon,\delta)$-Freudenthal Kantor triple systems with certain structure on the subspace $L_{-2}$ of the corresponding standard embedding five graded Lie (super)algebra $L(\epsilon,\delta):=L_{-2}\oplus L_{-1}\oplus L_0\oplus L_1\oplus L_2; [L_i,L_j]\subseteq L_{i+j}$. We recall Lie and Jordan structures associated with $(\epsilon,\delta)$-Freudenthal Kantor triple systems (see ref [26],[27]) and we give results for unitary and pseudo-unitary $(\epsilon,\delta)$-Freudenthal Kantor triple systems. Further, we give the notion of $\delta$-structurable algebras and connect them to $(-1,\delta)$-Freudenthal Kantor triple systems and the corresponding Lie (super) algebra construction.
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| 5. |
- Kamiya, Noriaki, et al.
(author)
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On anti-structurable algebras
- 2011
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In: RIMS Kokyuroku. - 1880-2818. ; 1769, s. 13-22
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Conference paper (peer-reviewed)
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| 6. |
- Kamiya, Noriaki, et al.
(author)
-
On anti-structurable algebras and extended Dynkin diagrams
- 2009
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279. ; 3:3, s. 183-190
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Journal article (peer-reviewed)abstract
- We construct Lie superalgebras osp(2n+1|4n+2) and osp(2n|4n) starting with certain classes of anti-structurable algebras via the standard embedding Lie superalgebra construction corresponding to (ε, δ)-Freudenthal Kantor triple systems.
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| 7. |
- Kamiya, Noriaki, et al.
(author)
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On constructions of Lie (super) algebras and (, Î)-Freudenthal-Kantor triple systems defined by bilinear forms
- 2020
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In: Journal of Algebra and Its Applications. - 0219-4988. ; 19:11
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Journal article (peer-reviewed)abstract
- In this work, we discuss a classification of (,Î)-Freudenthal-Kantor triple systems defined by bilinear forms and give all examples of such triple systems. From these results, we may see a construction of some simple Lie algebras or superalgebras associated with their Freudenthal-Kantor triple systems. We also show that we can associate a complex structure into these (,Î)-Freudenthal-Kantor triple systems. Further, we introduce the concept of Dynkin diagrams associated to such (,Î)-Freudenthal-Kantor triple systems and the corresponding Lie (super) algebra construction.
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| 8. |
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| 9. |
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| 10. |
- Kantor, Isaiah, et al.
(author)
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A Peirce decomposition for generalized Jordan triple systems of second order
- 2003
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In: Communications in Algebra. - 0092-7872. ; 31:12, s. 5875-5913
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Journal article (peer-reviewed)abstract
- Every tripotent e of a generalized Jordan triple system of second order uniquely defines a decomposition of the space of the triple into a direct sum of eight components. This decomposition is a generalization of the Peirce decomposition for the Jordan triple system. The relations between components are studied in the case when e is a left unit.
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