The theory of integrals is used to analyze the structure of Hopf algebroids. We prove that the total algebra of a Hopf algebroid is a separable extension of the base algebra if and only if it is a semi-simple extension and if and only if the Hopf algebroid possesses a normalized integral...
On the integrity of the dual algebra of some complete ultrametric Hopf algebras Aside from being without integral, on what other conditions a cocommutative Hopf algebra H is such that its dual H ' is an integral domainΦ We have no general answer to this question. However, it is well known...
The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations The Euclidean Hopf algebraUq(eN) dual of Fun(RNq■SOq1(N))is constructed by realizing it as a subalgebra of the differential algebra Diff(RNq) on the quant... Fiore,Gaetano - 《Journal of ...
Elliptic Quantum Groups $E_{au ,\\eta } (\\mathfrak{s}\\mathfrak{l}_2 )$ and Quasi-Hopf Algebras We construct an algebra morphism from the elliptic quantum group E t , h (\\frak sl 2) to a certain elliptic version of the "quantum loop groups in higher genus" studied by V. ...
摘要: In this thesis we introduce and study the class of h-local integral domains whose nonzero non-invertible ideals can be written as JP1 ···Pk with J an invertible ideal and P1, ..., Pk distinct ideals which are maximal among the nonzero non-invertible ideals of D....
This, in turn, is used to prove our final result: Suppose that if H is a finite dimensional semisimple cocommutative Hopf algebra over an algebraically closed field of positive characteristic. If R is an H -module algebra, then R is integral over R H , its subring of invariants....
A method is developed for investigating the Noetherian property of operators of a particular kind, prototypes of which are singular integral operators with a shift (SIOS). The algebra of symbols of SIOS is constructed. Questions of inver... YI Karlovich,VG Kravchenko - Mathematics of the USSR...
Access details : Access Details : Free Access Communications in Algebra On Hopf Algebras with Nonzero IntegralTaylor, PublisherCuadra, J
Factorization of the universal $\\mathcal R $ -matrix for ${U_q(\\widehat{sl}_2)} $ , , The factorization of the universal -matrix corresponding to the so-called Drinfeld Hopf structure is described in the example of the quantum affine algebra . As a result of the factorization proced...
We review Darboux‐Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux‐Crum transformation. We also consider conservation of...