Superspin chains solutions from 4D Chern-Simons theory by Y. Boujakhrout, E. H Saidi, R. Ahl Laamara, L. B Drissi

“…The oscillator realization of Lax operators solving the RLL relations of integrability is obtained in the gauge theory by extending the notion of Levi decomposition to Lie superalgebras. Based on particular 3-gradings of Lie superalgebras, we obtain graded oscillator Lax matrices for superspin chains with internal symmetries given by A(m − 1 | n − 1), B(m | n), C(n) and D(m | n).…”
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Kinematical superspaces by José Figueroa-O’Farrill, Ross Grassie

“…Abstract We classify N =1 d = 4 kinematical and aristotelian Lie superalgebras with spa- tial isotropy, but not necessarily parity nor time-reversal invariance. …”
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Supersymmetric Extensions of Non-Relativistic Scaling Algebras by Makoto Sakaguchi, Kentaroh Yoshida

“…We give a short summary on the classification of superalgebras with the anisotropic scaling as subalgebras of the following Lie superalgebras, psu(2,2|4), osp(8|4) and osp (8*|4), which appear in the study of AdS/CFT in type IIB string and M theories. …”
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On finite dimensional Nichols algebras of diagonal type by Nicolás Andruskiewitsch, Iván Angiono

“…Indeed the second part deals with Nichols algebras related to Lie algebras and superalgebras in arbitrary characteristic, while the third contains the information on Nichols algebras related to Lie algebras and superalgebras only in small characteristic, and the few examples yet unidentified in terms of Lie theory.…”
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N $$ \mathcal{N} $$ -extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions by Farhad Ali, Lucrezia Ravera

“…The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.…”
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On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions by Ricardo Caroca, Patrick Concha, Octavio Fierro, Evelyn Rodríguez

“…The super-$$BMS_3$$ BMS3 , the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. …”
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ON PRIMITIVE Zp-ALGEBRA by Ameer Jaber

“…Our main purpose is to provide for primitive associative Zp-algebras a structure theory analogous to that for algebras and superalgebras [1, 7, 8, 9, 10] and to classify primitive Zp-rings having a minimal one sided Zp-ideal.…”
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Fermionic shift symmetries in (anti) de Sitter space by James Bonifacio, Kurt Hinterbichler

“…For the particular case of AdS4, we look for non-trivial Lie superalgebras that can underly interacting theories that involve these fields. …”
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On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory by Axel de Goursac

“…In this paper, we review the three principal interpretations of this harmonic term: the Langmann-Szabo duality, the superalgebraic approach and the noncommutative scalar curvature interpretation. …”
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Diagrammatic state sums for 2D pin-minus TQFTs by Alex Turzillo

“…The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction generates pin-minus TQFTs, including the root invertible theory with partition function the Arf-Brown-Kervaire invariant. …”
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Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models by A. Hutsalyuk, A. Liashyk, S.Z. Pakuliak, E. Ragoucy, N.A. Slavnov

“…We study integrable models solvable by the nested algebraic Bethe ansatz and described by gl(2|1) or gl(1|2) superalgebras. We obtain explicit determinant representations for form factors of the monodromy matrix entries. …”
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Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian by Alexey Litvinov, Ilya Vilkoviskiy

“…Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras.…”
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Higgsed network calculus by Yegor Zenkevich

“…We also explain how quiver theories corresponding to Dynkin diagrams of superalgebras arise, write down the corresponding partition functions and W-algebras, and explain the connection with supersymmetric Macdonald-Ruijsenaars commuting Hamiltonians.…”
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LGU-Combined-Consciousness State Model by Shazia Rana, Muhammad Saeed, Florentin Smarandache

“…Hence, it is necessary to establish such superalgebraic structures that can organize and classify the uncertain and incomplete information floating in parallel higher dimensions as facts, events, or realities. …”
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Graded off-diagonal Bethe ansatz solution of the SU(2|2) spin chain model with generic integrable boundaries by Xiaotian Xu, Junpeng Cao, Yi Qiao, Wen-Li Yang, Kangjie Shi, Yupeng Wang

“…The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU(2|2) vertex model with both periodic and generic open boundary conditions are constructed. …”
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Classification of linearly compact simple algebraic N = 6 3-algebras by Cantarini, Nicoletta, Kac, Victor

“…In the present paper we classify algebraic linearly compact simple N = 6 3-algebras over an algebraically closed field of characteristic 0, using their correspondence with simple linearly compact Lie superalgebras with a consistent short ℤ-grading, endowed with a graded conjugation. …”
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Boost generator in AdS3 integrable superstrings for general braiding by Juan Miguel Nieto García, Alessandro Torrielli, Leander Wyss

“…We find that the boost coproducts are exact symmetries of the R-matrices we construct, besides fulfilling the relations of modified Poincaŕe-type superalgebras. In the process, we discover an ambiguity in determining the boost coproduct which allows us to derive differential constraints on our R-matrices. …”
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Super-Schwarzians via nonlinear realizations by Anton Galajinsky

“…Mathematicians like to think of them as the cocycles describing central extensions of Lie superalgebras. In this work, a third possibility is discussed which consists in applying the method of nonlinear realizations to osp(1|2) and su(1, 1|1) superconformal algebras. …”
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Lie algebra expansions, non-relativistic matter multiplets and actions by Oguzhan Kasikci, Mehmet Ozkan

“…Abstract We discuss a general methodology to provide rigid, off-shell matter multiplets and actions for recently constructed non-relativistic superalgebras. The technique is based on the Lie algebra expansion, which, in the context of supersymmetry, has so far been used to obtain non-relativistic on-shell supergravity models. …”
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Spin Hurwitz theory and Miwa transform for the Schur Q-functions by A. Mironov, A. Morozov, A. Zhabin

“…They appear in representation theory of the Sergeev group, which is a substitute of the symmetric group, related to the queer Lie superalgebras q(N). The corresponding spin Wˆ-operators were recently found in terms of time-derivatives, but a substitute of the Miwa parametrization remained unknown, which is an essential complication for the matrix model technique and further developments. …”
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