Related papers: BMS4 Algebra, Its Stability and Deformations

Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…

We show that there are four chiral ${\cal W}$-algebra extensions of $\mathfrak{so}(2,3)$ algebra and construct them explicitly. We do this by a simple identification of each of the inequivalent embeddings of a copy of…

We describe a new algebraic structure of "deformed chiral algebra" motivated by the study of the deformed W-algebras. We use it to gain some insights into the deformed Virasoro algebra.

It has recently been shown that the $W_3$ and $W_3^{(2)}$ algebras can be considered as subalgebras in some linear conformal algebras. In this paper we show that the nonlinear algebras $W_{2,4}$ and $WB_2$ as well as Zamolodchikov's spin…

This paper extends the correspondence between discrete Cluster Integrable Systems and BPS spectra of five-dimensional $\mathcal{N}=1$ QFTs on $\mathbb{R}^4\times S^1$ by proving that algebraic solutions of the integrable systems are exact…

Starting from flat two-dimensional gauge potentials we propose the notion of ${\cal W}$-gauge structure in terms of a nilpotent BRS differential algebra. The decomposition of the underlying Lie algebra with respect to an $SL(2)$ subalgebra…

In the author's article "Algebraic unsolvability of problem of absolute stability of desynchronized systems" (Automat. Remote Control 51 (1990), no. 6, pp. 754--759), it was shown that in general for linear desynchronized systems there are…

We study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of $S^2 \times S^2$. For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature…

We give an algebro-geometric or non-archimedean framework to study bubbling phenomena of Kahler metrics with Euclidean volume growth, after [DS17, Sun23, dBS23]. In particular, for any degenerating family to log terminal singularity, we…

We describe and study a four parameters deformation of the two products and the coproduct of the Hopf algebra of plane posets. We obtain a family of braided Hopf algebras, generally self-dual. We also prove that in a particular case (when…

Fix a weakly minimal (i.e., superstable $U$-rank $1$) structure $\mathcal{M}$. Let $\mathcal{M}^*$ be an expansion by constants for an elementary substructure, and let $A$ be an arbitrary subset of the universe $M$. We show that all…

The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that…

We describe the Lie algebra deformations of D=4 Maxwell superalgebra that was recently introduced as the symmetry algebra of a kappa-symmetric massless superparticle in a supersymmetric constant electromagnetic background. Further we…

This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension $15$ and decomposes into $3$ irreducible components…

We propose mixed boundary conditions for 3d conformal gravity consistent with variational principle in its second-order formalism that admit the chiral $\Lambda$-$\mathfrak{bms}_4$ algebra as their asymptotic symmetry algebra. This algebra…

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a…

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary…

We perform a classical BRST analysis of the symmetries corresponding to a generic $w_N$-algebra. An essential feature of our method is that we write the $w_N$-algebra in a special basis such that the algebra manifestly has a ``nested'' set…

We show that a wide class of $W$-(super)algebras, including $W_N^{(N-1)}$, $U(N)$-superconformal as well as $W_N$ nonlinear algebras, can be linearized by embedding them as subalgebras into some {\em linear} (super)conformal algebras with…

A dual weak brace is an algebraic structure $\left(S,\,+,\,\circ\right)$ including skew braces and giving rise to a set-theoretic solution of the Yang-Baxter equation. We show that such a map belongs to a family of set-theoretic solutions,…