Related papers: A Class of Numerical Semigroups Defined by Kunz an…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
We compute the quiver of any monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term…
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
We introduce partially multiplicative quandles (PMQ), a generalisation of both partial monoids and quandles. We set up the basic theory of PMQs, focusing on the properties of free PMQs and complete PMQs. For a PMQ $\mathcal{Q}$ with…
We develop a theory of general quotients for W- and Cu-semigroups beyond the case of quotients by ideals. To this end, we introduce the notion of a normal pair, which allows us to take quotients of W-semigroups in a similar way as normal…
A quantum symmetric pair consists of a quantum group $\mathbf U$ and its coideal subalgebra ${\mathbf U}^{\imath}_{\boldsymbol{\varsigma}}$ with parameters $\boldsymbol{\varsigma}$ (called an $\imath$quantum group). We initiate a Hall…
In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…
A quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all binary integer quadratic forms with semigroup property. If…
In a previous paper, the authors studied the radical filtration of a Weyl module $\Delta_\zeta(\lambda)$ for quantum enveloping algebras $U_\zeta(\overset\circ{\mathfrak g})$ associated to a finite dimensional complex semisimple Lie algebra…
Attached to a singular analytic curve germ in $d$-space is a numerical semigroup: a subset $S$ of the non-negative integers which is closed under addition and whose complement isfinite. Conversely, associated to any numerical semigroup $S$…
Quantum Steiffel manifolds were introduced by Vainerman and Podkolzin in \cite{VP}. They classified the irreducible representations of their underlying $C^*$-algebras. Here we compute the K groups of the quantum homogeneous spaces…
Semiclassical limits of generic multiparameter quantized coordinate rings A = O_q(k^n) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric…
A numerical semigroup is a co-finite submonoid of the monoid of non-negative integers under addition. Many properties of numerical semigroups rely on some fundamental invariants, such as, among others, the set of gaps (and its cardinality),…
The problem is the classification of the ideals of ``free differential algebras", or the associated quotient algebras, the q-algebras; being finitely generated, unital C-algebras with homogeneous relations and a q-differential structure.…
Let $G$ be the simple algebraic group $\mathrm{SL}_2$ defined over an algebraically closed field $k$ of characteristic $p > 0$. Using results of A. Parker, we develop a method which gives, for any $q \in \mathbb{N}$, a closed form…
We classify module categories over the category of representations of quantum $SL(2)$ in a case when $q$ is not a root of unity. In a case when $q$ is a root of unity we classify module categories over the semisimple subquotient of the same…
In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined…
We investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline{m}))$, introduced by Brzezi\'nski-Szyma\'nski as graph $C^*$-algebras. For $n\leq 3$, we give a number-theoretic invariant, when all but one weight are coprime to the order of…
Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity…