Related papers: Quantised coordinate rings of semisimple groups ar…
We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mathbb{C}(q)$. Moreover, we…
We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.
A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as a# b where a and b are elements of S and if, in addition, every element of S that is square…
In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our construction including the…
A subset $S$ of an integral domain is called a semidomain if the pairs $(S,+)$ and $(S\setminus\{0\}, \cdot)$ are commutative and cancellative semigroups with identities. The multiplication of $S$ extends to the group of differences…
Let $\mathfrak{g}$ be a semi-simple Lie algebra with fixed root system, and $U_q(\mathfrak{g})$ the quantization of its universal enveloping algebra. Let $\mathcal{S}$ be a subset of the simple roots of $\mathfrak{g}$. We show that the…
We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…
We show that R-matricies of all simple quantum groups have the properties which permit to present quantum group twists as transitions to other coordinate frames on quantum spaces. This implies physical equivalence of field theories…
In this article we study quotients of deformations of simple singularities, and attempt to characterize them in terms of subsystems of simple root systems. The quotient of a semiuniversal deformation of a simple singularity of inhomogeneous…
We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation. As an example, we turn the…
Important aspects of QCD factorization theorems are the properties of the objects involved that can be identified as universal. One example is that the definitions of parton densities and fragmentation functions for different types of…
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not…
In the realm of supercommutative superrings, this article investigates the unique factorization of elements. We build upon recent findings by Naser et. al. concerning similar results in noncommutative symmetric rings with zerodivisors,…
We propose the notion of partial resolution of a ring, which is by definition the endomorphism ring of a certain generator of the given ring. We prove that the singularity category of the partial resolution is a quotient of the singularity…
Let $F$ be an affine flat group scheme over a commutative ring $R$, and $S$ an $F$-algebra (an $R$-algebra on which $F$ acts). We define an equivariant analogue $Q_F(S)$ of the total ring of fractions $Q(S)$ of $S$. It is the largest…
For an integral domain $R$ and a commutative cancellative monoid $M$, the ring consisting of all polynomial expressions with coefficients in $R$ and exponents in $M$ is called the monoid ring of $M$ over $R$. An integral domain is called…
It is proved that the centre Z of the simply connected quantised universal enveloping algebra over C, U_{\e,P}(sl_n), \e a primitive l-th root of unity, l an odd integer >1, has a rational field of fractions. Furthermore it is proved that…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
Representations of small quantum groups $u_q({\mathfrak{g}})$ at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig…