The inhomogeneous invariance quantum supergroup of supersymmetry algebra

Altıntaş, Azmi Ali; Arık, M.

doi:10.1016/j.physleta.2008.07.070

Cited by 2 publications

(3 citation statements)

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“…As will be shown in our later sections, such quantum groups and their associated algebras need be extended to more general structures that involve supersymmetry, as for example in the case of quantum gravity or supergravity and superfield theories. Another important example of such quantum supergroups involves Drinfel'd 's quantum double construction and the R-matrix (e.g., as developed in [133] and subsequent reports related to quantum quasi-algebras [5,228,229]).…”

Section: Some Basic Examplesmentioning

confidence: 99%

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Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

Bâianu¹

2009

SIGMA

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Abstract. A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller effects, superfluidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions and supergravity. This approach requires a unified conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of nonAbelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. Fourier transforms, generalized FourierStieltjes transforms, and duality relations link, respectively, the quantum groups and quantum groupoids with their dual algebraic structures; quantum double constructions are also discussed in this context in relation to quasi-triangular, quasi-Hopf algebras, bialgebroids, Grassmann-Hopf algebras and higher dimensional algebra. On the one hand, this quantum algebraic approach is known to provide solutions to the quantum Yang-Baxter equation. On the other hand, our novel approach to extended quantum symmetries and their associated representations is shown to be relevant to locally covariant general relativity theories that are consistent with either nonlocal quantum field theories or local bosonic (spin) models with the extended quantum symmetry of entangled, 'string-net condensed' (ground) states. I.C. Baianu, J.F. Glazebrook and R. BrownKey words: extended quantum symmetries; groupoids and algebroids; quantum algebraic topology (QAT); algebraic topology of quantum systems; symmetry breaking, paracrystals, superfluids, spin networks and spin glasses; convolution algebras and quantum algebroids; nuclear Fréchet spaces and GNS representations of quantum state spaces (QSS); groupoid and functor representations in relation to extended quantum symmetries in QAT; quantization procedures; quantum algebras: von Neumann algebra factors; paragroups and Kac algebras; quantum groups and ring structures; Lie algebras; Lie algebroids; GrassmannHopf, weak C * -Hopf and graded Lie algebras; weak C * -Hopf algebroids; compact quantum groupoids; quantum groupoid C * -algebras; relativistic quantum gravity (RQG); supergravity and supersymmetry theories; fluctuating quantum spacetimes; intense gravitational fields; Hamiltonian algebroids in quantum gravity; Poisson-Lie manifolds and quantum gravity theories; quantum fundamental groupoids; tensor products of algebroids and categories; quantum double groupoids and algebroids; higher dimensional quantum symmetries; applications of generalized van Kampen theorem (GvKT) to quantum spacetime invariants

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Section: Some Basic Examplesmentioning

confidence: 99%

“…2.8 SU(3), SU (5), SU (10) and E 6 representations in quantum chromodynamics and unified theories involving spontaneous symmetry breaking…”

Section: Generalization Of the Quantum Yang-baxter Equationmentioning

confidence: 99%

Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

Bâianu¹

2009

SIGMA

View full text Add to dashboard Cite

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“…Woronowicz's approach [2] involves non-commutative co-multiplication and in Manin's approach [3] one can construct a quantum group by making linear transformations on quantum plane. Recently Manin's approach is used to find inhomogeneous invariance quantum groups of various particle algebras [4,5,6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%