相关论文: Truncation and duality results for Hopf image alge…

Non-anticommutative deformations have been studied in the context of supersymmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some…

We produce an explicit embedding of the planar algebra of the Drinfeld double of a finite-dimensional, semisimple and cosemisimple Hopf algebra $H$ into the two-cabling of the planar algebra of the dual Hopf algebra $H^*$ and characterise…

We consider two quantum phase spaces which can be described by two Hopf algebroids linked with the well-known $\theta_{\mu \nu }$-deformed $D=4$ Poincare-Hopf algebra $\mathbb{H}$. The first algebroid describes $\theta_{\mu \nu }$-deformed…

The Haar functional on the quantum $SU(2)$ group is the analogue of invariant integration on the group $SU(2)$. If restricted to a subalgebra generated by a self-adjoint element the Haar functional can be expressed as an integral with a…

We apply the theory of semiparametric estimation to a Hong-Ou-Mandel interference experiment with a spectrally entangled two-photon state generated by spontaneous parametric downconversion. Thanks to the semiparametric approach we can…

In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log…

Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two authors (TT and AVD). Integral theory and duality for those…

The 27-dimensional Hopf algebra A(F), defined by the exact sequence of quantum groups A(SL(2,C))->A(SL_q(2))->A(F), q^3=1, is studied as a finite quantum group symmetry of the matrix algebra M(3,C), describing the color sector of Alain…

In \cite{fl}, the authors get a new presentation of two-parameter quantum algebra $U_{v,t}(\mathfrak{g})$. Their presentation can cover all Kac-Moody cases. In this paper, we construct a suitable Hopf pairing such that $U_{v,t}(sl_{n})$ can…

Let $\mu$ and $\nu$ be fixed probability measures on a filtered space $(\Omega, {\cal F}, ({\cal F}_t)_{t\in {\bf R}^{+}})$. Denote by $\mu_T $ and $\nu_T $ (respectively, $\mu_{T-} $ and $\nu_{T-} $) the restrictions of the measures $\mu$…

We study algebraic locality principles on a 2+1D closed lattice in the presence of a Gauss law for a non-invertible symmetry. Prior work in arXiv:2509.03589 showed that when enforcing the Gauss law of an invertible symmetry, the principle…

We prove that every finite Borel measure $\mu$ in $\mathbb{R}^N$ that is bounded from above by the Hausdorff measure $\mathcal{H}^s$ can be split in countable many parts $\mu\lfloor_{E_k}$ that are bounded from above by the Hausdorff…

Let $\mu$ and $\nu$ be two Borel probability measures on two separable metric spaces $\X$ and $\Y$ respectively. For $h, g$ be two Hausdorff functions and $q\in \R$, we introduce and investigate the generalized pseudo-packing measure…

We discuss two-parameter deformations of an universal enveloping algebra $U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a finite-dimensional complex simple Lie algebra (or superalgebra). These deformations are Hopf algebras.…

In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These…

Motivated by the form of the noncommutative *-product in a system of open strings and Dp-branes with constant nonzero Neveu-Schwarz 2-form, we define a deformed multiplication operation on a quasitriangular Hopf algebra in terms of its…

In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a…

In the last decennia two generalizations of the Hopf algebra of symmetric functions have appeared and shown themselves important, the Hopf algebra of noncommutative symmetric functions NSymm and the Hopf algebra of quasisymmetric functions…

Let $\mathscr{M}$ be a $II_1$ factor acting on the Hilbert space $\mathscr{H}$, and $\mathscr{M}_{\textrm{aff}}$ be the Murray-von Neumann algebra of closed densely-defined operators affiliated with $\mathscr{M}$. Let $\tau$ denote the…

Multiplication by the pseudoscalar $\mathbf{I}$ has been traditionally used in geometric algebra to perform non-metric operations such as calculating coordinates and the regressive product. In algebras with degenerate metrics, such as…