N. Aizawa

activity

20232026

Z_{2}^{2}

-graded Extensions of the Liouville and Sinh-Gordon Theories

8 citations · 24 across the 7 of their papers we have counts for

collaborators

8 papers

nlin.SI2026

An integrable $Z_{2}^{2}$ -graded extension of Camassa-Holm equation and its bi-Hamiltonian structure

N. Aizawa, Ichi Fujii, Ren Ito +1

By constructing Lax operators in the loop algebra of the $Z_{2}^{2}$ -graded extension of the Lie superalgebra $osp (1∣2)$ , we derive a $Z_{2}^{2}$ -graded extens…

math-ph2025

Integrable $Z_{2}^{2}$ -graded super-Liouville Equation and Induced $Z_{2}^{2}$ -graded super-Virasoro Algebra

Naruhiko Aizawa, Ichi Fujii, Ren Ito +2

We present a framework for enlarging the construction of $Z_{2}^{2}$ -graded classical Toda theory from the class of $Z_{2}^{2}$ -graded Lie algebras to the class of $\math…

math-ph2025

An integrable hierarchy associated with loop extension of $Z_{2}^{2}$ -graded $osp (1∣2)$

N. Aizawa, I. Fujii, R. Ito

A hierarchy of $Z_{2}^{2}$ -graded integrable equations is constructed using the loop extension of the $Z_{2}^{2}$ -graded Lie superalgebra $osp (1∣2)$ . This hier…

math.GT2024★ 1 cited

Universal weight systems from a minimal $Z_{2}^{2}$ -graded Lie algebra

N. Aizawa, Daichi Kimura

Color Lie algebras, which were introduced by Ree, are a graded extension of Lie (super)algebras by an abelian group. We show that the color Lie algebras can be used to construct un…

math-ph2024★ 3 cited

Affine extensions of $Z_{2}^{2}$ -graded $os p (1∣2)$ and Virasoro algebra

N. Aizawa, J. Segar

It is known that there are two inequivalent $Z_{2}^{2}$ -graded $os p (1∣2)$ Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits t…

math-ph2024★ 8 cited

Integrable $Z_{2}^{2}$ -graded Extensions of the Liouville and Sinh-Gordon Theories

Naruhiko Aizawa, Ren Ito, Zhanna Kuznetsova +2

In this paper we present a general framework to construct integrable $Z_{2}^{2}$ -graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The s…

math-ph2024★ 5 cited

$N = 2$ Double graded supersymmetric quantum mechanics via dimensional reduction

N. Aizawa, Ren Ito, Toshiya Tanaka

We present a novel $N = 2$ $Z_{2}^{2}$ -graded supersymmetric quantum mechanics ( $Z_{2}^{2}$ -SQM) which has different features from those introduced so far. It…

math-ph2023★ 7 cited

$Z_{2}^{2}$ -graded supersymmetry via superfield on minimal $Z_{2}^{2}$ -superspace

N. Aizawa, Ren Ito, Toshiya Tanaka

A superfield formalism for the minimal $Z_{2}^{2}$ -graded version of supersymmetry is developed. This is done by using the recently introduced definition of integration on the…

An integrable Z22​-graded extension of Camassa-Holm equation and its bi-Hamiltonian structure

Integrable Z22​-graded super-Liouville Equation and Induced Z22​-graded super-Virasoro Algebra

An integrable hierarchy associated with loop extension of Z22​-graded osp(1∣2)

Universal weight systems from a minimal Z22​-graded Lie algebra

Affine extensions of Z22​-graded osp(1∣2) and Virasoro algebra

Integrable Z22​-graded Extensions of the Liouville and Sinh-Gordon Theories

N=2 Double graded supersymmetric quantum mechanics via dimensional reduction

Z22​-graded supersymmetry via superfield on minimal Z22​-superspace