Related papers: Integrable models and star structures
The properties of Hopf star operations and twisted Hopf stars operations on quantum groups are discussed in relation with the theory of representations (star representations). Invariant Hermitian sesquilinear forms (scalar products) on…
We investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
The representations of the pointed Hopf algebras $U$ and $\su$ are described, where $U$ and $\su$ can be regarded as deformations of the usual quantized enveloping algebras $U_q(\mathfrak{sl}(3))$ and the small quantum groups respectively.…
We study ideals in Hall algebras of monoid representations on pointed sets corresponding to certain conditions on the representations. These conditions include the property that the monoid act via partial permutations, that the…
The present article takes advantage of the properties of algebras in the category of S-modules (twisted algebras) to investigate further the fine algebraic structure of Hopf operads. We prove that any Hopf operad P carries naturally the…
This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…
We say that a Hopf algebra H is semicocommutative if the right adjoint coaction factorizes through the tensor product of H with the center of H. For instance the commutative and the cocommutative Hopf algebras are semicocommutative. The…
Poisson structures of the Poincar\'e group can be linked to deformations of the Minkowski space-time, classified some time ago by Zakrewski. Based on this classification, various quantum Minkowski space-times with coordinates Lie algebras…
In this work we apply the Drinfel'd twist of Hopf algebras to the study of deformed quantum theories. We prove that, by carefully considering the role of the central extension, it is indeed possible to construct the universal enveloping…
Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of…
The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by…
A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a representation…
We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted Hopf pairing. We state a Stone--von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg…
The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show,…
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This…
In the last decennia two generalizations of the Hopf algebra of symmetric functions have appeared and shown themselves important, the Hopf algebra of noncommutative symmetric functions NSymm and the Hopf algebra of quasisymmetric functions…
Tensor operators associated with a given quantum Lie algebra admit a natural description in the R-matrix language. Here we employ the R-matrix approach to discuss the problem of fusion of tensor operators. The most interesting case is…
q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a…