Algebraic Aspects of the Supersymmetric Minimal Surface Equation by Alfred Michel Grundland, Alexander Hariton

“…Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. …”
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Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system by Zengo Tsuboi

“…It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra Uq(gl(2r|1)(2)) and the non-twisted quantum affine algebra Uq(so(2r+1)(1)), we proposed, in the previous paper [1], a Wronskian solution of the T-system for Uq(so(2r+1)(1)) as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra Uq(gl(2r|1)(1)). …”
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Fermionization of fusion category symmetries in 1+1 dimensions by Kansei Inamura

“…When the symmetry of a bosonic TQFT is described by the representation category Rep(H) of a semisimple weak Hopf algebra H, the fermionized TQFT has a superfusion category symmetry SRep( H $$ \mathcal{H} $$ u ), which is the supercategory of super representations of a weak Hopf superalgebra H $$ \mathcal{H} $$ u . The weak Hopf superalgebra H $$ \mathcal{H} $$ u depends not only on H but also on a choice of a non-anomalous ℤ 2 subgroup of Rep(H) that is used for the fermionization. …”
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Essential Variational Poisson Cohomology by De Sole, Alberto, Kac, Victor

“…In the present paper we show that, for K skewadjoint, the Z -graded Lie superalgebra H[subscript K](V) is isomorphic to the finite dimensional Lie superalgebra [˜ over H](Nℓ,S) . …”
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Classification of Degenerate Verma Modules for E(5, 10) by Cantarini, Nicoletta, Caselli, Fabrizio, Kac, Victor

“…In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. …”
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More on the hidden symmetries of 11D supergravity by Laura Andrianopoli, Riccardo D'Auria, Lucrezia Ravera

“…In this paper we clarify the relations occurring among the osp(1|32) algebra, the M-algebra and the hidden superalgebra underlying the Free Differential Algebra of D=11 supergravity (to which we will refer as DF-algebra) that was introduced in the literature by D'Auria and Frè in 1981 and is actually a (Lorentz valued) central extension of the M-algebra including a nilpotent spinor generator, Q′. …”
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A note on de Finetti's lower probabilities and belief measures by Radko Mesiar

“…De Finetti has introduced lower and upper probabilities as boundary set functions when extending a fixed probability from an atomic algebra to an atomic superalgebra. We discuss the relationship of de Finetti’s lower and upper probabilities with belief and plausibility measures, and also investigate the order of their additivity. …”
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Induced N=2 composite supersymmetry in (2+1) dimensions by Alexandre, J, Mavromatos, N, Sarkar, S

“…Starting from N = 1 scalar supermultiplets in (2+1) dimensions, we build explicitly the composite superpartners which define an N = 2 superalgebra induced by the initial N = 1 supersymmetry. …”

Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics by Alexander A. Andrianov, Andrey V. Sokolov

“…When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. …”
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Chern–Simons–Antoniadis–Savvidy forms and standard supergravity by F. Izaurieta, P. Salgado, S. Salgado

“…In the context of the so called the Chern–Simons–Antoniadis–Savvidy (ChSAS) forms, we use the methods for FDA decomposition in 1-forms to construct a four-dimensional ChSAS supergravity action for the Maxwell superalgebra. On the another hand, we use the Extended Cartan Homotopy Formula to find a method that allows the separation of the ChSAS action into bulk and boundary contributions and permits the splitting of the bulk Lagrangian into pieces that reflect the particular subspace structure of the gauge algebra.…”
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The fine structure of the finite-size effects for the spectrum of the OSp(n|2m) spin chain by Holger Frahm, Márcio J. Martins

“…In this paper we investigate the finite-size properties of the spectrum of quantum spin chains with local spins taken to be the fundamental vector representation of the OSp(n|2m) superalgebra.…”
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Representations of superconformal algebras and mock theta functions by Wakimoto, M., Kac, Victor

“…However, in the case when g is a basic Lie superalgebra different from a simple Lie algebra or osp[subscript 1|n], modular invariance of normalized supercharacters of admissible [caret over g]-modules holds outside of boundary levels only after their modification in the spirit of Zwegers’ modification of mock theta functions. …”
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Three-dimensional extended Lifshitz, Schrödinger and Newton-Hooke supergravity by Nese Ozdemir, Mehmet Ozkan, Utku Zorba

“…Abstract We provide a systematic analysis of three-dimensional N $$ \mathcal{N} $$ = 2 extended Bargmann superalgebra and its Newton-Hooke, Lifshitz and Schrödinger extensions. …”
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Extended D = 3 Bargmann supergravity from a Lie algebra expansion by J.A. de Azcárraga, D. Gútiez, J.M. Izquierdo

“…In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from D=3, N=2 superPoincaré and its corresponding Chern-Simons supergravity.…”
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From sl_q(2) to a Parabosonic Hopf Algebra by Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov

“…Designated by sl_{−1}(2), this algebra encompasses the Lie superalgebra osp(1|2). It is obtained as a q=−1 limit of the sl_q(2) algebra and seen to be equivalent to the parabosonic oscillator algebra in irreducible representations. …”
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A SUPERINTEGRABLE MODEL WITH REFLECTIONS ON S^3 AND THE RANK TWO BANNAI-ITO ALGEBRA by Hendrik De Bie, Vincent Xavier Genest, Jean-Michel Lemay, Luc Vinet

“…It is shown that the Hamiltonian of the system can be constructed from the tensor product of four representations of the superalgebra osp(1|2) and that the superintegrability is naturally understood in that setting. …”
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Finite size and finite temperature studies of the osp(1|2) spin chain by T.S. Tavares, G.A.P. Ribeiro

“…We studied a quantum spin chain invariant by the superalgebra osp(1|2). We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behavior and we determined its central charge. …”
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Composite supersymmetries in low-dimensional systems by Alexandre, J, Mavromatos, N, Sarkar, S

“…We discuss an extension to a N = 2 superalgebra with central extension, due to the existence of topological currents in 2+1 dimensions. …”

Simplifying (super-)BMS algebras by Oscar Fuentealba, Marc Henneaux

“…Abstract We show that the non-linear BMS5 symmetry algebra of asymptotically flat Einstein gravity in five dimensions, as well as the super-BMS4 superalgebra of asymptotically flat supergravity, can be redefined so as to take a direct sum structure. …”
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Minimal AdS-Lorentz supergravity in three-dimensions by O. Fierro, F. Izaurieta, P. Salgado, O. Valdivia

“…The N=1 AdS-Lorentz superalgebra is studied and its relationship to semigroup expansion developed. …”
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