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.

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 A class of Hermitian generalized Jordan triple systems and Chern–Simons gauge theory

2014 ◽  
Vol 29 (29) ◽  
pp. 1450156
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple Systems ◽  
Fundamental Matter ◽  
Jordan Triple Systems ◽  
Chern Simons

We find a class of Hermitian generalized Jordan triple systems (HGJTSs) and Hermitian (ϵ, δ)-Freudenthal–Kantor triple systems (HFKTSs). We apply one of the most simple HGJTSs which we find to a field theory and obtain a typical u(N) Chern–Simons gauge theory with a fundamental matter.

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.

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 PLANAR HOMOLOGICAL MIRROR SYMMETRY

2007 ◽  
Vol 22 (29) ◽  
pp. 5351-5368 ◽  
Author(s):  
EIJI KONISHI
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Associative Algebra ◽  
String Field Theory ◽  
Mirror Symmetry ◽  
Open String ◽  
Homological Mirror Symmetry ◽  
Chern Simons

In this paper, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern–Simons-type topological open string field theory using homotopy associative algebra (A∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT duality of Dijkgraaf–Vafa theory.

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).

O(2) CHERN–SIMONS GAUGE THEORY AND Z2 ORBIFOLDS

1992 ◽  
Vol 07 (05) ◽  
pp. 1007-1023 ◽  
Author(s):  
KAORU AMANO ◽  
HIROSHI SHIROKURA
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Coherent State ◽  
Gauge Field ◽  
Three Dimensional ◽  
The State ◽  
Explicit Calculation ◽  
Gauge Field Theory ◽  
State Representation ◽  
Chern Simons

We quantize the three-dimensional O(2) pure Chern–Simons gauge field theory in a functional coherent-state representation. Both trivial and nontrivial flat O(2) bundles admit physical states. An explicit calculation relates the state functionals to the rational Z2-orbifold models.

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.

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