Related papers: Differential calculus on quantum groups: Construct…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
A short explanation of the complexity of the structure of Demailly-semple invariant jet differentials was given
On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the…
Some problems of the quantum error-correcting codes theory can be reduced to the investigation of the higher-rank numerical ranges of the operators related to the error operators. We constructively verify a conjecture on the structure of…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.
A Cartan Calculus of Lie derivatives, differential forms, and inner derivations, based on an undeformed Cartan identity, is constructed. We attempt a classification of various types of quantum Lie algebras and present a fairly general…
A method is given for obtaining equivalence subgroups of a family of differential equations from the equivalence group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
In this expository paper we explain in detail how to construct bicategorical colimits of several kinds of tensor categories, for example essentially small finitely cocomplete K-linear tensor categories. The constructions are direct and…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
This is a study of orbifold-quotients of quantum groups (quantum orbifolds $\Theta \rightrightarrows G_q$). These structures have been studied extensively in the case of the quantum $SU_2$ group. I will introduce a generalized mechanism…
An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.
We show that either of the two reasonable choices for the category of compact quantum groups is nice enough to allow for a plethora of universal constructions, all obtained "by abstract nonsense" via the adjoint functor theorem. This…
We define a categorical action of the shifted quantum loop group of $\mathfrak{sl}_2$ on the derived categories of Quot schemes of finite length quotient sheaves on a smooth projective curve. As an application, we obtain a semi-orthogonal…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…
Necessary and sufficient conditions are given for the construction of a hybrid quantum computer that operates on both continuous and discrete quantum variables. Such hybrid computers are shown to be more efficient than conventional quantum…