Related papers: Differential geometry of the q-superplane
We present several related examples of Hopf algebroids over a universal enveloping algebra which are of the scalar extension Hopf algebroid type and explain their origin in Lie and algebraic group theory.
We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2)…
By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually…
We recall the definition of $q$-differential algebras and discuss some representative examples. In particular we construct the $q$-analog of the Hochschild coboundary. We then construct the universal $q$-differential envelope of a unital…
Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…
We determine the additional structure which arises on the classical limit of a DQ-algebroid.
In Hopf-Galois theory, every $H$-Hopf-Galois structure on a field extension $K/k$ gives rise to an injective map $\mathcal{F}$ from the set of $k$-sub-Hopf algebras of $H$ into the intermediate fields of $K/k$. Recent papers on the failure…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
We re-examine all the contractions related with the ${\cal U}_q(su(2))$ deformed algebra and study the consequences that the contraction process has for their structure. We also show using ${\cal U}_q(su(2))\times{\cal U}(u(1))$ as an…
We extend the universal differential calculus on an arbitrary Hopf algebra to a ``universal Cartan calculus''. This is accomplished by introducing inner derivations and Lie derivatives which act on the elements of the universal differential…
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
In this Letter, we introduce the Hopf algebra structure of the quantum quaternionic group GL(1,H$_q)$ and discuss the isomorphism between the quantum symplectic group SP$_q(1)$ and the quantum unitary group SU$_q(2)$.
In this work we study the induction (induced and coinduced)theory for Hopf group coalgebra. We define a substructure B of a Hopf group coalgebra $H$, called subHopf group coalgebra. Also, we have introduced the definition of Hopf group…
In this paper we give an extension of the Cartier-Gabriel-Kostant structure theorem to Hopf algebroids.
The theory of integrals is used to analyse the structure of Hopf algebroids, introduced in math.QA/0302325. We prove that the total algebra of the Hopf algebroid is a separable extension of the base algebra if and only if it is a…
The extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ is quantized from three different points of view in this paper, which produces three noncommutative and noncocommutative Hopf algebra structures, and yield other three…
We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum…
We first give a pedagogical introduction to the differential calculus on q-groups and analize the relation between differential calculus and q-Lie algebra. Equivalent definitions of bicovariant differential calculus are studied and their…
Higher extensions and higher central extensions, which are of importance to non-abelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf…