Nonsemisimple Quantum Groups as Hopf Algebras of the Dual Functions
نویسنده
چکیده
The simple (or semisimple) classical Lie groups (algebras) may be transformed by contractions to the nonsemisimple ones of the different structure. We named the set of such groups (algebras) as Cayley-Klein (CK) groups (algebras). In our approach [2] the contractions of the groups (algebras) are described with the help of dual valued parameters, i.e. the nonsemisimple CK groups are regarded as the groups over an associative algebra Dn(ι; C) with the nilpotent generators ιk, ι 2 k = 0, k = 1, ..., n satisfying the commutative low of multiplications ιkιm = ιmιk 6= 0, k 6= m. The general element of the dual algebra Dn(ι; C) have the form
منابع مشابه
Algebras and Hopf Algebras in Braided Categories
This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, as well as colour-Lie algebras. Basic facts about braided categories C are recalled, the modules and comodules of Hopf algebras in such categories are studied, the notion of ‘braided-commutative’ or ‘braided-cocommutative’ Hop...
متن کاملColoured quantum universal enveloping algebras
We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called colour group. Such transformations are labelled by some colour parameters, taking values in a colour set C. We show that vario...
متن کاملRooted Trees and Symmetric Functions: Zhao’s Homomorphism and the Commutative Hexagon
Recent work in perturbative quantum field theory has led to much study of the Connes-Kreimer Hopf algebra. Its (graded) dual, the Grossman-Larson Hopf algebra of rooted trees, had already been studied by algebraists. L. Foissy introduced a noncommutative version of the Connes-Kreimer Hopf algebra, which turns out to be self-dual. Using some homomorphisms defined by the author and W. Zhao, we de...
متن کاملReiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
متن کامل
Hopf Galois Extensions, Triangular Structures, and Frobenius Lie Algebras in Prime Characteristic
The final goal of this paper is to introduce certain finite dimensional Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic p > 0. The antipodes of these Hopf algebras have order either 2p or 2, and in the minimal dimension p there exists just one Hopf algebra in this class which coincides with an example due to Radford [35] of a Hopf algebra with a no...
متن کامل