相关论文: Braided Oscillators
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…
We briefly review some recent results concerning algebraical (oscillator) aspects of the $N$-body single-species and multispecies Calogero models in one dimension. We show how these models emerge from the matrix generalization of the…
We briefly report on our result that the braided tensor product algebra of two module algebras $A_1,A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $H_1$ with a subalgebra isomorphic to $A_2$…
We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and differential operations on forms, we obtain the structure…
The notion of a coherent unit action on algebraic operads was first introduced by Loday for binary quadratic nonsymmetric operads and generalized by Holtkamp, to ensure that the free objects of the operads carry a Hopf algebra structure.…
A realization of various algebraic structures in terms of the $C_{\lambda}$-extended oscillator algebras is introduced. In particular, the $C_{\lambda}$-extended oscillator algebras realization of Fairlie-Fletcher-Zachos (FFZ)algebra is…
The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying…
We describe a class of examples of braided monoidal categories which are built from Hopf algebras in symmetric categories. The construction is motivated by a calculation in two-dimensional conformal field theory and is tailored to contain…
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian…
The quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one.
We apply the operadic modeling of brace $B_{\infty}$ algebras, as developed by Gerstenhaber and Voronov, to the context of Hopf algebroids in the sense of Xu. Specifically, we construct a strict $B_{\infty}$ isomorphism between the type I…
We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two…
We study braided Hochschild and cyclic homology of ribbon algebras in braided monoidal categories, as introduced by Baez and by Akrami and Majid. We compute this invariant for several examples coming from quantum groups and braided groups.
In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the…
In braided tensor categories we show the Maschke's theorem and give the necessary and sufficient conditions for double cross biproducts and crossbiproducts and biproducts to be bialgebras. We obtain the factorization theorem for braided…
We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on…
We introduce and study symmetric and exterior algebras in braided monoidal categories such as the category O for quantum groups. We relate our braided symmetric algebras and braided exterior algebas with their classical counterparts.
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
We consider the Hopf algebra of B-diagrams as an algebra projecting onto the Heisenberg algebra and designed to encode the combinatorics of the bosonic normal-ordering problem. In order to understand and generalize the properties of the…