相关论文: Addendum to "On Super-Jordanian ${\cal U}_{\sf h}(…

The Jordanian deformation of $sl(2)$ bi-algebra structure is studied in view of physical applications to breaking of conformal symmetry in the high energy asymptotics of scattering. Representations are formulated in terms of polynomials,…

Let $\cal{A}$ be the algebra of quaternions $\mathbb{H}$ or octonions $\mathbb{O}$. In this manuscript a new proof is given, based on ideas of Cauchy and D' Alembert, of the fact that an ordinary polynomial $f(t) \in {\cal{A}}\, [t]$ has a…

Fock space representations of the Lie superalgebra $sl(n+1|m)$ and of its quantum analogue $U_q[sl(n+1|m)]$ are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The…

Errors in the published version of the paper are corrected, and new figures are provided.

We describe degenerations of three-dimensional Jordan superalgebras over $\mathbb{C}$. In particular, we describe all irreducible components in the corresponding varieties.

Recent results on the Racah algebra $\mathcal{R}_n$ of rank $n - 2$ are reviewed. $\mathcal{R}_n$ is defined in terms of generators and relations and sits in the centralizer of the diagonal action of $\mathfrak{su}(1,1)$ in…

We give an explicit presentation of the module of differentials of order $n$ of a finitely generated algebra via a higher-order Jacobian matrix. We use the presentation to study some aspects of this module in the case of hypersurfaces. More…

This is the Reply to the revised Comment [Phys. Rev. Lett. 102, 139601; arXiv:0810.4791] by Joachim Krug on our paper: C. Escudero, Phys. Rev. Lett. 100, 116101 (2008); arXiv:0804.1898.

In this paper, we introduce an algebra $\mathcal{H}$ from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra $\mathcal{H}$ and the…

We give a complete classification in canonical forms on finite-dimensional vector spaces over the real numbers.

We briefly comment on a paper by Rubano and Scudellaro [astro-ph/0103335] where they found general exact solutions for two classes of exponential potentials in a scalar field model for quintessence. In that paper the authors were led to…

After the rejection of their comment [arXiv:cond-mat/0609399v1] to our Phys. Rev. Lett. {\bf 97}, 100601 (2006), the Authors informed us that an extended version of their comment is going to be published in a different journal under the…

Let G be a linear algebraic group defined over a field k. We prove that, under mild assumptions on k and G, there exists a finite k-subgroup S of G such that the natural map H^1(K, S) -> H^1(K, G) is surjective for every field extension…

We comment on the paper ``Numerical study of the SWKB condition of novel classes of exactly solvable systems'' [Y. Nasuda and N. Sawado, Mod. Phys. Lett. A 36, 2150025 (2021)]. We show that it misrepresents our prior work [J. Bougie, A.…

By adapting the classical proof of Jordan's theorem on finite subgroups of linear groups, we show that every approximate subgroup of the unitary group U_n(C) is almost abelian.

We argue whether physics of universal approach of Severyukhin et al. [arXiv:1703.05710] is approved.

In this note we confront the research conducted in \cite{Hoang:2017suc} with results previously obtained by the author, and critically examine some of their claimed findings.

Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…

This is a corrigendum to Acta Math. 196 (2006) as well as to the follow-up publications JFA 259 (2010) and to JFA 260 (2011).

We give the realizations of the extended Weyl-Heisenberg (WH) algebra and the Rubakov-Spiridonov (RS) superalgebra in terms of anyons, characterized by the statistical parameter $\nu\in[0,1]$, on two-dimensional lattice. The construction…