共查询到20条相似文献,搜索用时 31 毫秒
1.
Zai-Zhe Zhong 《International Journal of Theoretical Physics》1999,38(2):519-524
The problem of how to obtain a hyperboliccomplexification of a Hopf algebra from two known Hopfalgebras is discussed. We prove that this Hopf algebrais isomorphic to a direct sum of the two known Hopf algebras, and that therefore this direct sum isalso a Hopf algebra. In particular, the result can beapplied to quantum enveloping algebras. 相似文献
2.
Walter D. van Suijlekom 《Communications in Mathematical Physics》2009,290(1):291-319
We study the structure of renormalization Hopf algebras of gauge theories. We identify certain Hopf subalgebras in them, whose
character groups are semidirect products of invertible formal power series with formal diffeomorphisms. This can be understood
physically as wave function renormalization and renormalization of the coupling constants, respectively. After taking into
account the Slavnov–Taylor identities for the couplings as generators of a Hopf ideal, we find Hopf subalgebras in the corresponding
quotient as well. In the second part of the paper, we explain the origin of these Hopf ideals by considering a coaction of
the renormalization Hopf algebras on the Batalin-Vilkovisky (BV) algebras generated by the fields and couplings constants.
The so-called classical master equation satisfied by the action in the BV-algebra implies the existence of the above Hopf
ideals in the renormalization Hopf algebra. Finally, we exemplify our construction by applying it to Yang–Mills gauge theory. 相似文献
3.
We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair in involution, consisting of a group-like element and a character. This provides the key construction for allowing the extension of cyclic cohomology to Hopf algebras in the nonunimodular case and, further, to developing a theory of characteristic classes for actions of Hopf algebras compatible not only with traces but also with the modular theory of weights. This applies to both ribbon and coribbon algebras as well as to quantum groups and their duals. 相似文献
4.
Stefan Weinzierl 《Frontiers of Physics》2016,11(3):111206
In this paper I discuss Hopf algebras and Dyson–Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson–Schwinger equations. 相似文献
5.
We show that the q-deformed Heisenberg algebras have not the Hopf algebraic structure when q take generics values, but when q is a root of unity, there exist Hopf algebraic structures in the q-deformed Heisenberg algebras. 相似文献
6.
We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted pairing. We state a Stone–von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg double and deduce the effect on the algebra of shifting the product and coproduct of the original twisted Hopf algebra. We conclude by showing that the quantum Weyl algebra, quantum Heisenberg algebras, and lattice Heisenberg algebras are all examples of the general construction. 相似文献
7.
Suemi Rodríguez-Romo 《Foundations of Physics》1996,26(11):1457-1468
We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived. 相似文献
8.
Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a simple comultiplication for the quantum current operators. In this Letter, we will present a generalization of such a realization of quantum Hopf algebras. As a special case, we will choose the structure functions for this algebra to be elliptic functions to derive certain elliptic quantum groups as a Hopf algebra, which degenerates into quantum affine algebras if we take certain degeneration of the structure functions. 相似文献
9.
Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their actions on algebras allows the expansion of the range of applications of cyclic cohomology. It is the goal of this Letter to illustrate these recent developments, with special emphasis on the application to transverse index theory, and point towards future directions. In particular, we highlight the remarkable accord between our framework for cyclic cohomology of Hopf algebras on the one hand and both the algebraic as well as the analytic theory of quantum groups on the other, manifest in the construction of the modular square. 相似文献
10.
We prove that there is a Hopf duality between two Hopf algebras built on rooted trees: the Connes–Kreimer Hopf algebra HR which controls the renormalization in quantum field theory, and the Grossman–Larson Hopf algebra A introduced ten years ago through some 'differential' and combinatorial reason. We then study two natural operators on A, inspired by similar ones introduced by Connes and Kreimer for HR. 相似文献
11.
We describe Hopf algebras which are central extensions of quantum current groups. For a special value of the central charge, we describe Casimir elements in these algebras. New types of generators for quantum current algebra and its central extension for quantum simple Lie groups, are obtained. The application of our construction to the elliptic case is also discussed. 相似文献
12.
We review the algebraic structures imposed on the renormalization procedure in terms of Hopf and Lie algebras of Feynman graphs, and exhibit the connection to diffeomorphisms of physical observables. 相似文献
13.
Letters in Mathematical Physics - We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of... 相似文献
14.
We construct the induced representations of the null-plane quantum Poincaré and quantum kappa Galilei algebras in (1+1) dimensions. The induction procedure makes use of the concept of module and is based on the existence of a pair of Hopf algebras with a nondegenerate pairing and dual bases. 相似文献
15.
This Letter examines the question of the structure of the Hopf algebra deformations of the universal enveloping algebras of the simple Lie algebras. Deformations of a complex algebra A are viewed as algebras defined over formal power series rings that specialize to A when the parameters go to 0. Only the case of U(sl(2,C)) is treated but the methods are general. Under the Ansatz that the two Borel subalgebras are deformed as Hopf algebras but possibly differently, we construct a universal two-parameter deformation. 相似文献
16.
We construct symmetric monoidal categories of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the
notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of , are dual to the corresponding Connes-Kreimer Hopf algebras on rooted trees and Feynman diagrams. We thus obtain an interpretation
of the Connes-Kreimer Lie algebras on rooted trees and Feynman graphs as Ringel-Hall Lie algebras. 相似文献
17.
We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the theory of twisted graded traces and their associated twisted cyclic cocycles. One of our principal results is a new method of constructing differential calculi, using twisted graded traces. 相似文献
18.
We introduce the concept of para-Hopf algebroid and define their cyclic cohomology in the spirit of Connes–Moscovici cyclic cohomology for Hopf algebras. Para-Hopf algebroids are closely related to, but different from, Hopf algebroids. Their definition is motivated by attempting to define a cyclic cohomology theory for Hopf algebroids in general. We show that many of Hopf algebraic structures, including the Connes–Moscovici algebra
, are para-Hopf algebroids 相似文献
19.
We introduce two types of algebras which include respectively the well known reflection equation (RE) and Faddeev-Reshetikhin-Takhtayan
algebras associated with a quasitriangular Hopf algebraH. We show that these two types of algebras are twist-equivalent. It follows that a RE algebra is a module algebra over a twisted
tensor square ofH. We present some applications to the equivariant quantization.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. 相似文献
20.
A. A. Vladimirov 《Zeitschrift fur Physik C Particles and Fields》1993,58(4):659-663
We reformulate the method recently proposed for constructing quasitriangular Hopf algebras of the quantum-double type from theR-matrices obeying the Yang-Baxter equations. Underlying algebraic structures of the method are elucidated and an illustration of its facilities is given. The latter produces an example of a new quasitriangular Hopf algebra. The corresponding universal?-matrix is presented as a formal power series. 相似文献