34 citations · 97 across the 7 of their papers we have counts for
7 papers
Irreducible representations of -graded supersymmetry algebra and -graded supermechanics
N. Aizawa, S. Doi
Irreducible representations (irreps) of -graded supersymmetry algebra of are obtained by the method of induced representation and they are used to deri…
Comments of -supersymmetry in superfield formalism
S. Doi, N. Aizawa
We investigate superfield formulation of the minimal -supersymmetry. It is shown that the integrability on -superspace guarantees the invariance of…
Classification of the Reducible Verma Modules over the Jacobi Algebra
N. Aizawa, V. K. Dobrev, S. Doi
In the present paper we study the representations of the Jacobi algebra. More concretely, we define, analogously to the case of semi-simple Lie algebras, the Verma modules over the…
-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
Shunya Doi, Naruhiko Aizawa
Quantum mechanical systems whose symmetry is given by -graded version of superconformal algebra are introduced. This is done by finding a realization of a $\mathbb{…
-Graded extensions of supersymmetric quantum mechanics via Clifford algebras
N. Aizawa, K. Amakawa, S. Doi
It is shown that the supersymmetric quantum mechanics (SQM) can be extended to a -graded superalgebra. This is done by presenting quantum mechanical mo…
-Extension of duble-graded supersymmetric and superconformal quantum mechanics
N. Aizawa, K. Amakawa, S. Doi
In the recent paper, Bruce and Duplij introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an extension of Lie superalgebraic nature of …
Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type
N. Aizawa, K. Amakawa, S. Doi
We present a relationship between the Calogero-Moser particles confined in harmonic oscillator potentials and a representation theory of the infinite dimensional Lie algebra which…