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Susumu Okubo

Publications and source records attributed to Susumu Okubo.

29 records · Page 2Linked to original sources
arXiv2005

Lie algebras with S4-action and structurable algebras

The normal symmetric triality algebras (STA's) and the normal Lie related triple algebras (LRTA's) have been recently introduced by the second author, in connection with the principle of triality. It turns out that the unital normal LRTA's are precisely the structurable algebras extensively studied by Allison. It will be shown that the normal STA's (respectively LRTA's) are the algebras that coordinatize those Lie algebras whose automorphism group contains a copy of the alternating (resp. symmetric) group of degree 4.

math.RA↗
arXiv2003

Construction of Lie Superalgebras from Triple Product Systems

Any simple Lie superalgebras over the complex field can be constructed from some triple systems. Examples of Lie superalgebras $D(2,1;α)$, G(3) and F(4) are given by utilizing a general construction method based upon $(-1,-1)$ balanced Freudenthal-Kantor triple system.

math-ph↗
arXiv2003

Global Symmetries of Time-Dependent Schrodinger Equations

Some symmetries of time-dependent Schrödinger equations for inverse quadratic, linear, and quadratic potentials have been systematically examined by using a method suitable to the problem. Especially, the symmetry group for the case of the linear potential turns out to be a semi-direct product $SL(2,R) x T_2(R)$ of the $SL(2,R)$ with a two-dimensional real translation group $T_2(R)$. Here, the time variable $t$ transforms as $t \to t^\prime = (ct+d)/(at+b)$ for real constants $a, b, c$, and $d$ satisfying $bc - ad =1$ with an accompanying transformation for the space coordinate $x$.

math-ph↗
arXiv2001

Orthonormal Eigenbases over the Octonions

We previously showed that the real eigenvalues of 3x3 octonionic Hermitian matrices form two separate families, each containing 3 eigenvalues, and each leading to an orthonormal decomposition of the identity matrix, which would normally correspond to an orthonormal basis. We show here that it nevertheless takes both families in order to decompose an arbitrary vector into components, each of which is an eigenvector of the original matrix; each vector therefore has 6 components, rather than 3.

math.RA↗
arXiv1997

Angular Momentum, Quaternion, Octonion, and Lie-Super Algebra osp(1,2)

We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same method will lead to the Lie-super algebra osp(1,2). Also, the quantum generalization of the method is discussed on the basis of the quantum group $su_q(2)$.

math-ph↗
arXiv1997

Lorentz-Invariant Hamiltonian and Riemann Hypothesis

We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to infinite-dimensional representation of the Lorentz group have many interesting properties. Especially, a relationship exists between the zero zeta function condition and the absence of trivial representations in the wave function.

quant-ph↗
arXiv1994

Representations of Clifford Algebras and its Applications

A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple system in terms of 8-component spinors associated with the Clifford algebras $C(0,7)$ and $C(4,3)$.

hep-th↗
arXiv1994

New Link Invariants and Yang-Baxter Equation

We have new solutions to the Yang-Baxter equation, from which we have constructed new link invariants containing more than two arbitrary parameters. This may be regarded as a generalization of the Jones' polynomial. We have also found another simpler invariant which discriminates only the linking structure of knots with each other, but not details of individual knot.

hep-th↗
arXiv1994

Some New Solutions of Yang-Baxter Equation

We have found some new solutions of both rational and trigonometric types by rewriting Yang-Baxter equation as a triple product equation in a vector space of matrices.

hep-th↗