Beyond the 10-fold Way: 13 Associative $$ {\mathbb Z}_2\times {\mathbb Z}_2$$-Graded Superdivision Algebras

Kuznetsova, Z.; Toppan, Francesco

doi:10.1007/s00006-023-01263-1

Cited by 3 publications

(3 citation statements)

References 36 publications

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“…This suggests the existence of a new class of integrable systems characterized by Z 2 2 -supersymmetry. We also mention that a classification of Z 2 2 -superdivision algebras has been made [36]. It is an interesting problem how the new superdivision algebras relate to other mathematics or nature just as we have observed in the 10-fold way.…”

Section: Introductionmentioning

confidence: 68%

Integration on minimal Z22 -superspace and emergence of space

Aizawa,

Ito

2023

J. Phys. A: Math. Theor.

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We investigate the possibilities of integration on the minimal Z2 2-superspace. Two definitions are taken from the works by Poncin and Schouten and we examine their generalizations. It is shown that these definitions impose some restrictions on the integrable functions. We then introduce a new definition of integral, which is inspired by our previous work, and show that the definition does not impose restrictions on the integrable functions. An interesting feature of this definition is the emergence of a spatial coordinate which means that the integral is defined on R<sup>2 despite the fact that the (0,0) part of the minimal Z2 2-superspace is R

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Section: Introductionmentioning

confidence: 68%

Integration on minimal Z22 -superspace and emergence of space

Aizawa,

Ito

2023

J. Phys. A: Math. Theor.

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“…This implies the possibility of experimental realization of 2 2 -graded para-particles. (e) super division algebras [29].…”

Section: 2mentioning

confidence: 99%

“…There is no reason to stop at 2 -grading, one may consider n 2 -graded division algebras and would expect surprising connection with other objects. In [29], a classification of 2 2 -graded division algebras has been done. It was shown that there are 13 2 2 -graded division algebras in addition to the 2 -graded counterpart.…”

Section: 2mentioning

confidence: 99%

Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications

Aizawa

2023

SciPost Phys. Proc.

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We give a brief review on recent developments of \mathbb{Z}_2^nℤ2n-graded symmetry in physics in which hidden \mathbb{Z}_2^nℤ2n-graded symmetries and \mathbb{Z}_2^nℤ2n-graded extensions of known systems are discussed. This elucidates physical relevance of the \mathbb{Z}_2^nℤ2n-graded algebras. As an example of physically interesting algebra, we take \mathbb{Z}_2^2ℤ22-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for N = 1, 2N=1,2 algebras is presented and as an application of the irreps, \mathbb{Z}_2^2ℤ22-graded SUSY classical actions are constructed.

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