0 Decoupling Braided Tensor Factors ∗
نویسندگان
چکیده
We briefly report on our result [9] that the braided tensor product algebra of two module algebras A1,A2 of a quasitriangular Hopf algebra H is equal to the ordinary tensor product algebra of A1 with a subalgebra isomorphic to A2 and commuting with A1, provided there exists a realization of H within A1. As applications of the theorem we consider the braided tensor product algebras of two or more quantum group covariant quantum spaces or deformed Heisenberg algebras. ∗Talk given at the 23-rd International Conference on Group Theory Methods in Physics, Dubna (Russia), August 2000
منابع مشابه
Decoupling of Tensor factors in Cross Product and Braided Tensor Product Algebras
We briefly review and illustrate our procedure to ‘decouple’ by transformation of generators: either a Hopf algebra H from a Hmodule algebra A1 in their cross-product A1>⊳H; or two (or more) H-module algebras A1,A2. These transformations are based on the existence of an algebra map A1>⊳H → A1. Preprint 02-64 Dip. Matematica e Applicazioni, Università di Napoli DSF/29-2002 ∗Contribution to the P...
متن کاملHopf Galois Extension in Braided Tensor Categories
The relation between crossed product and H-Galois extension in braided tensor categories is established. It is shown that A = B#σH is a crossed product algebra if and only if the extension A/B is Galois, the inverse can of the canonical morphism can factors through object A⊗B A and A is isomorphic as left B-modules and right H-comodules to B⊗H in braided tensor categories. For the Yetter-Drinfe...
متن کاملOn the Braiding on a Hopf Algebra in a Braided Category
By definition, a bialgebra H in a braided monoidal category (C, τ) is an algebra and coalgebra whose multiplication and comultiplication (and unit and counit) are compatible; the compatibility condition involves the braiding τ . The present paper is based upon the following simple observation: If H is a Hopf algebra, that is, if an antipode exists, then the compatibility condition of a bialgebr...
متن کاملThe Erwin Schrr Odinger International Institute for Mathematical Physics Q{epsilon Tensor for Quantum and Braided Spaces Q-epsilon Tensor for Quantum and Braided Spaces
The machinery of braided geometry introduced previously is used now to construct thètotally antisymmetric tensor' on a general braided vector space determined by R-matrices. This includes natural q-Euclidean and q-Minkowski spaces. The formalism is completely covariant under the corresponding quantum group such as g SO q (4) or g SO q (1; 3). The Hodge operator and diierentials are also constru...
متن کاملUnbraiding the braided tensor product
We show that the braided tensor product algebra A1⊗A2 of two module algebras A1,A2 of a quasitriangular Hopf algebraH is equal to the ordinary tensor product algebra of A1 with a subalgebra of A1⊗A2 isomorphic to A2, provided there exists a realization of H within A1. In other words, under this assumption we construct a transformation of generators which ‘decouples’ A1,A2 (i.e. makes them commu...
متن کامل