• Corpus ID: 244799712

# Beyond the $10$-fold way: $13$ associative $Z_2\times Z_2$-graded superdivision algebras

@inproceedings{Kuznetsova2021BeyondT,
title={Beyond the \$10\$-fold way: \$13\$ associative \$Z\_2\times Z\_2\$-graded superdivision algebras},
author={Zhanna Kuznetsova and Francesco Toppan},
year={2021}
}
• Published 1 December 2021
• Mathematics
The “10-fold way” refers to the combined classification of the 3 associative division algebras (of real, complex and quaternionic numbers) and of the 7, Z2-graded, superdivision algebras (in a superdivision algebra each homogeneous element is invertible). The connection of the 10-fold way with the periodic table of topological insulators and superconductors is well known. Motivated by the recent interest in Z2 × Z2-graded physics (classical and quantum invariant models, parastatistics) we…

## References

SHOWING 1-10 OF 36 REFERENCES
Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications
• Mathematics
• 2021
This paper presents the classification, over the fields of real and complex numbers, of the minimal Z2 × Z2-graded Lie algebras and Lie superalgebras spanned by 4 generators and with no empty graded
${\mathcal N}$ -extension of double-graded supersymmetric and superconformal quantum mechanics
• Physics, Mathematics
• 2019
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 ${\cal N}=1$ SQM to a
The Z_2 x Z_2-graded Lie superalgebra pso(2m+1|2n) and new parastatistics representations
• Mathematics
• 2017
When the relative commutation relations between a set of m parafermions and n parabosons are of relative parafermion type'', the underlying algebraic structure is the classical orthosymplectic Lie
Twisted Equivariant Matter
• Mathematics, Physics
• 2012
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical threefold way of real/complex/
Z2*Z2-graded Lie symmetries of the Levy-Leblond equations
• Mathematics
• 2016
This paper exhaustively investigates the symmetries of the $(1+1)$-dimensional L\'evy-Leblond Equations, both in the free case and for the harmonic potential, and introduces a new feature, explaining the existence of first-order differential symmetry operators not entering the super Schr\"odinger algebra.
A Taste of Jordan Algebras
In this book, Kevin McCrimmon describes the history of Jordan Algebras and he describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim
A quantum mechanical model that realizes the $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features