q-Lorentz group and braided coaddition onq-Minkowski space

Meyer, Ulrich

doi:10.1007/bf02101550

Cited by 22 publications

(31 citation statements)

References 15 publications

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“…Then we identify the image m ± = Sl ∓ in the conventional notation of [31], where S is the antipode of U q (g). Other examples of interest include the q-Lorentz group dual pair [32]. Proof We cast the construction in [5] into the present weakly quasitriangular setting.…”

Section: The Cross Relations and Coproductmentioning

confidence: 99%

Double-bosonization of braided groups and the construction of U_q(g)

Majid

1999

Math. Proc. Camb. Phil. Soc.

106

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We introduce a quasitriangular Hopf algebra or 'quantum group' U (B), the double-bosonisation, associated to every braided group B in the category of Hmodules over a quasitriangular Hopf algebra H, such that B appears as the 'positive root space', H as the 'Cartan subalgebra' and the dual braided group B * as the 'negative root space' of U (B). The choice B = f recovers Lusztig's construction of U q (g), where f is Lusztig's algebra associated to a Cartan datum; other choices give more novel quantum groups. As an application, our construction provides a canonical way of building up quantum groups from smaller ones by repeatedly extending their positive and negative root spaces by linear braided groups; we explicitly construct U q (sl 3 ) from U q (sl 2 ) by this method, extending it by the quantum-braided plane A 2 q . We provide a fundamental representation of U (B) in B. A projection from the quantum double, a theory of double biproducts and a Tannaka-Krein reconstruction point of view are also provided.

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Section: The Cross Relations and Coproductmentioning

confidence: 99%

Double-bosonization of braided groups and the construction of U_q(g)

Majid

1999

Math. Proc. Camb. Phil. Soc.

106

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“…An essential observation is that coproducts of coordinates imply their translations [23,41,44,46,57,58]. This can be seen as follows.…”

Section: Definition and Basic Properties Of Q-deformed Translationsmentioning

confidence: 99%

ANALYSIS ON q-DEFORMED QUANTUM SPACES

Wachter

2007

Int. J. Mod. Phys. A

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A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and selfcontained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, qdeformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces. *

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“…The present approach does not yield bicovariant calculi, but can be applied to all bosonisations, for instance as well to the quantum Poincaré group considered in Ref. 6.…”

Section: Applicationmentioning

confidence: 99%