Related papers: $H_D$-Quantum Vertex Algebras
We give a systematic construction of Hopf algebra structures on braided cofree coalgebras. The relevant underlying structures are braided algebras and braided coalgebras. We provide some interesting examples of these algebras and coalgebras…
It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A_1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space.
Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco…
We prove the existence of a universal braided compact quantum group acting on a graph $\mathrm{C}^*$-algebra in the category of $\mathbb{T}$-$\mathrm{C}^*$-algebras with a twisted monoidal structure, in the spirit of the seminal work of S.…
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
An algebraic analysis framework for quantum calculus is proposed. The quantum derivative operator $D_{\tau ,\sigma}$ is based on two commuting bijections $\tau$ and $\sigma$ defined on an arbitrary set $M$ equipped with a tension structure…
In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its quantum Miura tranformation. The vertex operators for this $\hbar$-deformed $W_{N}$ algebra and its commutation relations are also obtained.
We introduce a twisted quantum affine algebra associated to each simply laced finite dimensional simple Lie algebra. This new algebra is a Hopf algebra with a Drinfeld-type comultiplication. We obtain this algebra by considering its vertex…
Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be…
We extend the bicharacter construction of quantum vertex algebras first proposed by Borcherds to the case of super Hopf algebras. We give a bicharacter description of the charged free fermion super vertex algebra, which allows us to…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
We propose a new non-commutative generalization of the representation variety and the character variety of a knot group. Our strategy is to reformulate the construction of the algebra of functions on the space of representations in terms of…
The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is…
Associated to each subset $J$ of the nodes $I$ of a Dynkin diagram is a triangular decomposition of the corresponding Lie algebra $\mathfrak{g}$ into three subalgebras $\widetilde{\mathfrak{g}_{J}}$ (generated by $e_{j}$, $f_{j}$ for $j\in…
We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…
A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…
We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on…