A triality Group of nonassociative algebras with involution
This paper is to study for local triality relations and ist global relations That is, this is a generalization of automorhisms and derivations.
math.RA↗
arXiv subjects
Noriaki Kamiya
Publications and source records attributed to Noriaki Kamiya.
Dynamical Yang-Baxter maps and Hopf algebroids associated with s-sets
An s-set is an algebraic generalization of the regular s-manifold introduced by Kowalski, one of the generalized symmetric spaces in differential geometry. We prove that suitable s-sets give birth to dynamical Yang-Baxter maps, set-theoretic solutions to a version of the quantum dynamical Yang-Baxter equation. As an application, Hopf algebroids and rigid tensor categories are constructed by means of these dynamical Yang-Baxter maps.
math.QA↗
Algebras Satisfying Triality and S_4-symmetry
We give a review of recent works for non-associative algebras, especially Lie algebras satisfying the triality relation. They are also intimately related to S_4 (symmetric group of 4-objects) symmetry of the Lie algebras.
math-ph↗
A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory
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.
hep-th↗
Triality, Structurable and Pre-structurable Algebras
We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.
math.RA↗
Left unital Kantor triple systems and structurable algebras
Left unital Kantor triple systems will be shown to correspond to structurable algebras endowed with an involutive automorphism. A related result is proved for (-1,-1) Freudenthal-Kantor triple systems. Some consequences for the associated 5-graded Lie algebras and superalgebras are deduced too. In particular, left unital (-1,-1) Freudenthal-Kantor triple systems are shown to be intimately related to Lie superalgebras graded over the root system of type B(0,1).
math.RA↗
(-1,-1)-Balanced Freudenthal Kantor triple systems and noncommutative Jordan algebras
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of characteristic zero, the simple noncommutative Jordan algebras of this type are classified.
math.RA↗
A Peirce decomposition for generalized Jordan triple systems of second order
A tripotent of a generalized triple system of second order defines a decomposition of the space of the space which consist of 10 components. It gives a generalization of the Peirce decomposition n for the Jordan triple system which consists in general of 4 components.
math.RA↗
Quasi-Classical Lie-Super Algebra and Lie-Super Triple Systems
Notions of quasi-classical Lie-super algebra as well as Lie-super triple systems have been given and studied with some examples. Its application to Yang-Baxter equation has also been given.
q-alg↗