Pieri Formulae and Specialisation of Super Jacobi Polynomials by Sergeev, Alexander Nikolaevich, Zharinov, Egor D.

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Completeness of Bethe Ansatz for Gaudin Models with 𝔤𝔩(1|1) Symmetry and Diagonal Twists by Kang Lu

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Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of GL(1|1) and (C3 + A) by Ali Eghbali, Tayebe Parvizi, Adel Rezaei-Aghdam

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A family of regular vertex operator algebras with two generators by Adamović Dražen

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AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit by Lucrezia Ravera

“…In this paper, we present the construction of the three-dimensional Chern-Simons supergravity theory invariant under the so-called AdS Carroll superalgebra, which was obtained in the literature as a contraction of the AdS superalgebra. …”
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SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions by Jean Thierry-Mieg, Peter Jarvis

“…Abstract We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform A ˜ $$ \tilde{A} $$ mixing exterior-forms of all degrees and satisfying the chiral self-duality condition A ˜ = ∗ A ˜ χ $$ \tilde{A} =^{\ast }{\tilde{A}}_{\chi } $$ , where χ denotes the superalgebra grading operator. …”
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Classical Lie bialgebras for AdS/CFT integrability by contraction and reduction by Niklas Beisert, Egor Im

“…The two major steps in this construction consist in the contraction to a 3D Poincaré superalgebra and a certain reduction to a deformation of the $\mathfrak{u}(2|2)$ superalgebra. …”
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New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions by Yao-Zhong Zhang, Jason L. Werry

“…Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. …”
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Three-dimensional exotic Newtonian supergravity theory with cosmological constant by Patrick Concha, Lucrezia Ravera, Evelyn Rodríguez

“…The underlying new non-relativistic superalgebra is obtained by expanding the $${\mathcal {N}}=2$$ N = 2 AdS superalgebra and can be written as two copies of the enhanced Nappi–Witten algebra, one of which is augmented by supersymmetry. …”
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Conformal higher-spin symmetries in twistor string theory by D.V. Uvarov

“…It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains psl(4|4,R) superalgebra. …”
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Exceptional super Yang-Mills in 27 + 3 and worldvolume M-theory by Michael Rios, Alessio Marrani, David Chester

“…A particularly interesting case occurs in signature D=27+3, where the superalgebra is centrally extended by an electric 11-brane and its 15-brane magnetic dual. …”
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Carrollian and non-relativistic Jackiw–Teitelboim supergravity by Lucrezia Ravera, Utku Zorba

“…The extended Newton–Hooke structure, and, in particular, the invariant metric necessary for the BF construction of non-relativistic JT supergravity, is obtained by performing an expansion of the $$\mathcal {N}=2$$ N = 2 AdS $$_2$$ 2 superalgebra. Subsequently, we introduce the extended AdS $$_2$$ 2 Carroll superalgebra, and the associated invariant metric, as a suitable redefinition of the extended Newton–Hooke superalgebra. …”
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The linear $\protect \mathfrak{n}(1|N)$–invariant differential operators and $\protect \mathfrak{n}(1|N)$–relative cohomology by Khalfoun, Hafedh, Laraiedh, Ismail

“…Over the $(1,N)$-dimensional supercircle $S^{1|N}$, we classify $\mathfrak{n}(1|N)$-invariant linear differential operators acting on the superspaces of weighted densities on $S^{1|N}$, where $\mathfrak{n}(1|N)$ is the Heisenberg Lie superalgebra. This result allows us to compute the first differential $\mathfrak{n}(1|N)$-relative cohomology of the Lie superalgebra $\mathcal{K}(N)$ of contact vector fields with coefficients in the superspace of weighted densities. …”
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Non-relativistic three-dimensional supergravity theories and semigroup expansion method by Patrick Concha, Marcelo Ipinza, Lucrezia Ravera, Evelyn Rodríguez

“…Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. …”
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The variational Poisson cohomology by De Sole, Alberto, Kac, Victor

“…In the first part of the paper we explain how to introduce various cohomology complexes, including Lie superalgebra and Poisson cohomology complexes, and basic and reduced Lie conformal algebra and Poisson vertex algebra cohomology complexes, by making use of the corresponding universal Lie superalgebra or Lie conformal superalgebra. …”
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Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space by R. R. Metsaev

“…Abstract Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. …”
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On the Maxwell supergravity and flat limit in 2 + 1 dimensions by Patrick Concha, Diego M. Peñafiel, Evelyn Rodríguez

“…The flat limit is applied at the level of the superalgebra, Chern–Simons action, supersymmetry transformation laws and field equations.…”
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Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics by Martin Cederwall, Jakob Palmkvist

“…The relevant underlying algebraic structure turns out to be a tensor hierarchy algebra rather than a Borcherds superalgebra. This tensor hierarchy algebra is a non-contragredient superalgebra, generically infinite-dimensional, which is a double extension of the structure algebra of the extended geometry. …”
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Nonlinear symmetries of perfectly invisible PT-regularized conformal and superconformal mechanics systems by Juan Mateos Guilarte, Mikhail S. Plyushchay

“…The PT-regularized superconformal mechanics systems in the phase of the unbroken exotic nonlinear N $$ \mathcal{N} $$ = 4 super-Poincaré symmetry are described by nonlinearly super-extended Schrödinger algebra with the osp(2|2) sub-superalgebra. In the partially broken phase, the scaling dimension of all odd integrals is indefinite, and the osp(2|2) is not contained as a sub-superalgebra.…”
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A note on q-oscillator realizations of Uq(gl(M|N)) for Baxter Q-operators by Zengo Tsuboi

“…We consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra Uq(gl(M|N)), and obtain q-oscillator realizations of the contracted algebras proposed in [1]. …”
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