Algebraic generalization of quantum statistics

Stoilova, N. I.; Jeugt, J. Van der

doi:10.1088/1742-6596/128/1/012061

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…where A(m − 1, n − 1) designates sl m|n which we will focus on here. Several results about these graded algebras and their quantization were obtained in the Lie superalgebra literature; they generalise the bosonic-like ones; some of them will be commented in this study, related others are described in literature; see for instance [42][43][44][45][46].…”

Section: Chern-simons With Gauge Supergroupsmentioning

confidence: 88%

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Lax operator and superspin chains from 4D CS gauge theory

Youssra¹,

Saidi²,

Laamara³

et al. 2022

J. Phys. A: Math. Theor.

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We study the properties of interacting line defects in the four-dimensional Chern Simons gauge theory with invariance given by the SL (m|n) super-group family. From this theory, we derive the oscillator realisation of the Lax operator for superspin chains with SL(m|n) symmetry. To this end, we investigate the holomorphic property of the bosonic Lax operator and build a diﬀerential equation describing the RLL eqs veriﬁed by this operator in the framework of the 4D CS gauge theory. We generalize this construction to the case of gauge super-groups, and develop a super-Dynkin diagram algorithm to deal with the decomposition of the Lie superalgebras. We obtain the generalisation of the Lax operator describing the interaction between the electric Wilson super-lines and the magnetic 't Hooft super-defects. This coupling is given in terms of a mixture of bosonic and fermionic oscillator degrees of freedom in the phase space of magnetically charged 't Hooft super-lines. The purely fermionic realisation of the superspin chain Lax operator is also investigated and it is found to coincide exactly with the ℤ2- gradation of Lie superalgebras.

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Section: Chern-simons With Gauge Supergroupsmentioning

confidence: 88%

“…(2) It offers a guiding algorithm to extend the Levi-decomposition to Lie superalgebras, which to our knowledge, is still an open problem [44,45]. Because of this lack, we will use this algorithm later on when we study the extension of the Levi-decomposition to sl(m|n).…”

Section: • Levi-decomposition In D-languagementioning

confidence: 99%

Lax operator and superspin chains from 4D CS gauge theory

Youssra¹,

Saidi²,

Laamara³

et al. 2022

J. Phys. A: Math. Theor.

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Parafermions for higher order extensions of the Poincaré algebra and their associated superspace

Campoamor-Stursberg¹,

Traubenberg²

2009

J. Phys. A: Math. Theor.

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Parafermions of order two and three are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincaré algebra. The corresponding superfields are constructed, and some of their main properties analyzed in detail. In this context, the existence problem of operators acting like covariant derivatives is analyzed, and the associated operators are explicitly constructed. *

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Algebraic generalization of quantum statistics

Cited by 2 publications

References 24 publications

Lax operator and superspin chains from 4D CS gauge theory

Lax operator and superspin chains from 4D CS gauge theory

Parafermions for higher order extensions of the Poincaré algebra and their associated superspace

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