Related papers: Hopf algebras of canonical commutation relations
It is known that there is a Hopf algebra structure on the vector space with basis all heap-ordered trees. We give a new bialgebra structure on the space with basis all permutations and show that there is a direct bialgebra isomorphism…
We characterize Hopf spaces with finitely generated cohomology as an algebra over the Steenrod algebra. We "deconstruct" the original space into an H-space Y with finite mod p cohomology and a finite number of p-torsion Eilenberg-Mac Lane…
A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…
This work introduces a novel $q$-$\hbar$ deformation of the Heisenberg algebra, designed to unify and extend several existing $q$-deformed formulations. Starting from the canonical Heisenberg algebra defined by the commutation relation…
We construct quantum commutators on module-algebras of quasi-triangular Hopf algebras. These are quantum-group covariant, and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy…
For each $\ell\geq 1$ and $\lambda,\mu\in\Bbbk$, we study the representations of a family of pointed Hopf algebras $\mathcal{A}_{\lambda,\mu}$. These arise as Hopf cocycle deformations of the graded algebra $\mathcal{FK}_3\#\Bbbk…
A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a…
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and…
The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups…
A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
We study the Hopf equation which is equivalent to the pentagonal equation, from operator algebras. A FRT type theorem is given and new types of quantum groups are constructed. The key role is played now by the classical Hopf modules…
The finite dual $H^{\circ}$ of an affine commutative-by-finite Hopf algebra $H$ is studied. Such a Hopf algebra $H$ is an extension of an affine commutative Hopf algebra $A$ by a finite dimensional Hopf algebra $F$. The main theorem gives…
We consider "Hopfological" techniques as in \cite{Ko} but for infinite dimensional Hopf algebras, under the assumption of being co-Frobenius. In particular, $H=k[{\mathbb Z}]\#k[x]/x^2$ is the first example, whose corepresentations category…
We discuss a general construction of a deformation of a smash product algebra coming from an action of a particular Hopf algebra. This Hopf algebra is generated by skew-primitive and group-like elements, and depends on a complex parameter.…
In recent years, growing attention has been devoted to the possibility that theories with deformed symmetries, associated with certain models of non-commutative spacetime, may encode a fundamental form of decoherence. This effect should be…
We study the quantization of a linear scalar field, whose symmetries are described by the kappa-Poincare' Hopf-algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (planckian) cut-off for…
Given a scalar parameter $q$, the $q$-deformed Heisenberg algebra $\mathcal{H}(q)$ is the unital associative algebra with two generators $A,B$ that satisfy the $q$-deformed commutation relation $AB-qBA= I$, where $I$ is the multiplicative…
We investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…