Related papers: String Quantization and the Shuffle Hopf Algebra

We use modular invariant theory to establish a complete set of relations of the mod $p$ homology of $\{QS^k\}_{k\geq0}$, for $p$ odd, as a ring object in the category of coalgebras (also known as a coalgebraic ring or a Hopf ring). We also…

The generalized Cartan type $\mathbf{S}$ Lie algebras in char 0 with the Lie bialgebra structures involved are quantized, where the Drinfel'd twist we used is proved to be a variation of the Jordanian twist. As the passage from char 0 to…

We extend the Hopf algebra description of a simple quantum system given previously, to a more elaborate Hopf algebra, which is rich enough to encompass that related to a description of perturbative quantum field theory (pQFT). This provides…

Definitions of the parastatistics algebras and known results on their Lie (super)algebraic structure are reviewed. The notion of super-Hopf algebra is discussed. The bosonisation technique for switching a Hopf algebra in a braided category…

The dynamics of the 3 dimensional perfect fluid is equivalent to the motion of vortex filaments or "strings". We study the action principle and find that it is described by the Hopf term of the nonlinear sigma model. The Poisson bracket…

We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as examples. It is shown to be the bosonization of the quantum…

Given a simple Lie algebra $\mathfrak{g}$ and an element $\mu\in\mathfrak{g}^*$, the corresponding shift of argument subalgebra of $\text{S}(\mathfrak{g})$ is Poisson commutative. In the case where $\mu$ is regular, this subalgebra is known…

We use categorical description of the invariant 2-cohomology group of Hopf algebra to compute such cohomology for two finite dimensional Hopf algebras: the group ring of $Z_8\rtimes Aut(Z_8)$ and Kac-Paljutkin algebra. For the first of…

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…

Let $ G^\tau $ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfeld structure of Poisson group; let $ H^\tau $ be its dual Poisson group. By means of Drinfeld's double construction and…

We study maximal Poisson-commutative subalgebras in the Poisson algebra $S(\mathfrak{g})$ of a semisimple Lie algebra $\mathfrak{g}$ constructed by Mischenko and Fomenko with the help of the argument shift method. We prove that these…

We introduce the notions of Hopf quasigroup and Hopf coquasigroup $H$ generalising the classical notion of an inverse property quasigroup $G$ expressed respectively as a quasigroup algebra $k G$ and an algebraic quasigroup $k[G]$. We prove…

After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and…

We show that Hopf invariants, defined by evaluation in Harrison cohomology of the commutative cochains of a space, calculate the logarithm map from a fundamental group to its Malcev Lie algebra. They thus present the zeroth Harrison…

A class of nongraded Hamiltonian Lie algebras was earlier introduced by Xu. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a ``sandwich'' method…

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there…

For an associative algebra $A$, the famous theorem of Loday, Quillen and Tsygan says that there is an isomorphism between the graded symmetric product of the cyclic homology of $A$ and the Lie algebra homology of the infinite matrices…

Action of finite-dimensional Hopf algebra $H$ on commutative $k-$algebra $A$ is considered. As a generalization of the well-known fact for finite groups S. Montgomery raised a problem in 1993 whether $A$ is integral over subalgebra of…

We construct explicit Drinfel'd twists for the generalized Cartan type $H$ Lie algebras in characteristic $0$ and obtain the corresponding quantizations and their integral forms. Via making modular reductions including modulo $p$ reduction…

Multiple Eisenstein series are holomorphic functions in the complex upper-half plane, which can be seen as a crossbreed between multiple zeta values and classical Eisenstein series. They were originally defined by Gangl-Kaneko-Zagier in…