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Let S be a monoidal category with equalizers that are preserved by the tensor
product. The notion of categories internal to S is defined, generalizing the notions
of monoid and comonoid in S, and ex...
The classical identities between the q-binomial coefficients and factorials can be gener-
alized to a context where numbers are replaced by braids. More precisely, for every pair i, n of
natural num...
Derivations and Projections on Jordan Triples. An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis
Derivations and Projections Jordan Triples nonassociative algebra continuous cohomology quantum functional analysis Operator Algebras
2012/6/19
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-1...
In this paper we realize some powers of Dedekind \eta-function as the trace of an operator on quantum coordinate algebras.
Skew monoidales, skew warpings and quantum categories
bialgebroid fusion operator quantum category monoidal bicategory monoidale skew-monoidal category
2012/5/9
Kornel Szlach\'anyi recently used the term skew-monoidal category for a particular laxified version of monoidal category. He showed that bialgebroids $H$ with base ring $R$ could be characterized in t...
Loewy filtration and quantum de Rham cohomology over quantum divided power algebra
quantum divided power algebra Loewy filtration socle radical rigidity q-differentials
2012/4/18
As a continuation of \cite{HU}, we explore the submodule structures of the quantum divided power algebra $\mathcal{A}_q(n)$ introduced in \cite{HU} and its truncated objects $\mathcal{A}_q(n, \bold m)...
Golden Quantum Oscillator and Binet-Fibonacci Calculus
Golden Quantum Oscillator Binet-Fibonacci Calculus Quantum Algebra
2011/9/19
Abstract: The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases $q=\phi$ and $Q=-1/\phi$. Quantum harmonic oscillator for this Golden calc...
Abstract: Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular...
Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Quantum grassmannians quantum Richardson varieties quantum toric varieties straightening laws standard monomials
2011/8/29
Abstract: In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum anal...
A generalized Steinberg section and branching rules for quantum groups at roots of 1
generalized Steinberg section branching rules quantum groups
2011/8/23
Abstract: 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 applica...
A new dynamical reflection algebra and related quantum integrable systems
new dynamical reflection algebra quantum integrable systems
2011/7/7
We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, an...
Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
Quantum-to-Classical Correspondence Hubbard-Stratonovich Dynamical Systems
2011/3/2
We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-St...
Manin triples and differential operators on quantum groups
Manin triples differential operators quantum groups
2011/1/18
Let (a,m, l) be a Manin triple, and let M, L be algebraic groups with Lie algebras m, l respectively. We point out that the product M×L carries a natural structure of Poisson manifold,whose Poisson te...
Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
Classical quantum behavior integrated density of states randomly perturbed lattice
2011/1/20
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single...
Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols
Quantum Network Coding Schemes Classical Nonlinear Protocols
2011/3/3
The k-pair problem in network coding theory asks to send k messages simultaneously between k
source-target pairs over a directed acyclic graph. In a previous paper [ICALP 2009, Part I, pages 622–633]...