scholarly journals Quadratic Jordan Triple Systems

2019 ◽  
Vol 11 (2) ◽  
pp. 68
Author(s):  
Amir Baklouti
Keyword(s):  
Triple System ◽  
Triple Systems ◽  
Jordan Triple System ◽  
Jordan Triple Systems ◽  
Dimension One

In this work, We show that every Jordan triple system can be viewed as a T∗extension of another one or an ideal of co-dimension one of a Jordan triple system whose represent the T∗extension of another Jordan triple system. Moreover, several result involving the structure of quadratic Jordan triple systems are given.

Hermitian generalized Jordan triple systems and certain applications to field theory

2014 ◽  
Vol 29 (13) ◽  
pp. 1450071 ◽  
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Triple Systems ◽  
Jordan Triple System ◽  
Mathematical Properties ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian generalized Jordan triple systems and prove a structure theorem. We also give some examples of the systems and study mathematical properties. We apply a Hermitian generalized Jordan triple system to a field theory and obtain a Chern–Simons gauge theory.

Representations of simple anti-Jordan triple systems of m × n matrices

2017 ◽  
Vol 16 (05) ◽  
pp. 1750093 ◽  
Author(s):  
Hader A. Elgendy
Keyword(s):  
Triple System ◽  
Closed Field ◽  
Monomial Basis ◽  
Triple Systems ◽  
Infinite Dimensional ◽  
Matrix Algebras ◽  
Jordan Triple System ◽  
Finite Dimensional ◽  
Jordan Triple Systems

We show that the universal associative envelope of the simple anti-Jordan triple system of all [Formula: see text] ([Formula: see text] is even, [Formula: see text]) matrices over an algebraically closed field of characteristic 0 is finite-dimensional. The monomial basis and the center of the universal envelope are determined. The explicit decomposition of the universal envelope into matrix algebras is given. The classification of finite-dimensional irreducible representations of an anti-Jordan triple system is obtained. The semi-simplicity of the universal envelope is shown. We also show that the universal associative envelope of the simple polarized anti-Jordan triple system of [Formula: see text] matrices is infinite-dimensional.

scholarly journals A STRUCTURE THEORY OF (−1,−1)-FREUDENTHAL KANTOR TRIPLE SYSTEMS

2009 ◽  
Vol 81 (1) ◽  
pp. 132-155 ◽  
Author(s):  
NORIAKI KAMIYA ◽  
DANIEL MONDOC ◽  
SUSUMU OKUBO
Keyword(s):  
Triple System ◽  
Lie Superalgebras ◽  
Structure Theory ◽  
Triple Systems ◽  
Jordan Triple System

AbstractIn 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 (ε,δ)-Freudenthal Kantor triple system. Further, we introduce the notion of δ-structurable algebras and connect them to (−1,δ)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction.

Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 281-292 ◽  
Author(s):  
Marina Tvalavadze
Keyword(s):  
Associative Algebra ◽  
Triple System ◽  
Universal Enveloping Algebras ◽  
Triple Systems ◽  
Enveloping Algebras ◽  
Injective Homomorphism ◽  
Pbw Basis ◽  
Finite Dimensional ◽  
Jordan Triple Systems ◽  
Kirillov Dimension

In this work we are concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system (AJTS). We prove that if 𝕋 is a triple system as above, then there exists an associative algebra U(𝕋) and an injective homomorphism ε : 𝕋 → U(𝕋), where U(𝕋) is an AJTS under the triple product defined by (a,b,c) = abc - cba. Moreover, U(𝕋) is a universal object with respect to such homomorphisms. We explicitly determine the PBW-basis of U(𝕋), the center Z(U(𝕋)) and the Gelfand-Kirillov dimension of U(𝕋).

scholarly journals Hermitian(ϵ,δ)-Freudenthal-Kantor Triple Systems and Certain Applications of*-Generalized Jordan Triple Systems to Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Higgs Mechanism ◽  
The Novel ◽  
Yang Mills ◽  
Triple Systems ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian(ϵ,δ)-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of theu(N)⊕u(M)andsp(2N)⊕u(1)Hermitian 3-algebras. We apply a*-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit.

scholarly journals Triality Groups Associated with Triple Systems and their Homotope Algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Noriaki Kamiya
Keyword(s):  
Lie Algebras ◽  
Triple System ◽  
Simple Lie Algebras ◽  
Triple Systems ◽  
Jordan Triple System

Abstract We introduce the notion of an (α, β, γ) triple system, which generalizes the familiar generalized Jordan triple system related to a construction of simple Lie algebras. We then discuss its realization by considering some bilinear algebras and vice versa. Next, as a new concept, we study triality relations (a triality group and a triality derivation) associated with these triple systems; the relations are a generalization of the automorphisms and derivations of the triple systems. Also, we provide examples of several involutive triple systems with a tripotent element.

Catalytic Activity of Binary and Triple Systems Based on Redox Inactive Metal Compound, LiSt and Additives of Monodentate Ligands-Modifiers: DMF, HMPA and PhOH, in Selective Ethylbenzene Oxidation with Dioxygen

2016 ◽  
Vol 10 (3) ◽  
pp. 259-270
Author(s):  
Ludmila Matienko ◽  
◽  
Larisa Mosolova ◽  
Vladimir Binyukov ◽  
Gennady Zaikov ◽  
...  
Keyword(s):  
Catalytic Activity ◽  
Triple System ◽  
Metal Compound ◽  
Ethylbenzene Oxidation ◽  
Catalytic Systems ◽  
Triple Systems ◽  
Lithium Compound ◽  
Mechanism Of Catalysis ◽  
Monodentate Ligands

Mechanism of catalysis with binary and triple catalytic systems based on redox inactive metal (lithium) compound {LiSt+L2} and {LiSt+L2+PhOH} (L2=DMF or HMPA), in the selective ethylbenzene oxidation by dioxygen into -phenylethyl hydroperoxide is researched. The results are compared with catalysis by nickel-lithium triple system {NiII(acac)2+LiSt+PhOH} in selective ethylbenzene oxidation to PEH. The role of H-bonding in mechanism of catalysis is discussed. The possibility of the stable supramolecular nanostructures formation on the basis of triple systems, {LiSt+L2+PhOH}, due to intermolecular H-bonds, is researched with the AFM method.

scholarly journals Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs

2010 ◽  
Vol 62 (2) ◽  
pp. 355-381 ◽  
Author(s):  
Daniel Král’ ◽  
Edita Máčajov´ ◽  
Attila Pór ◽  
Jean-Sébastien Sereni
Keyword(s):  
Triple System ◽  
Steiner Triple System ◽  
Cubic Graphs ◽  
Steiner Triple Systems ◽  
Cubic Graph ◽  
Triple Systems ◽  
Forbidden Configurations ◽  
Edge Colourings

AbstractIt is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations.Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph G is S-edge-colourable for a Steiner triple system S if its edges can be coloured with points of S in such a way that the points assigned to three edges sharing a vertex form a triple in S. Among others, we show that all cubic graphs are S-edge-colourable for every non-projective nonaffine point-transitive Steiner triple system S.

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