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Braided groups and algebraic quantum field theories

โœ Scribed by Shahn Majid


Publisher
Springer
Year
1991
Tongue
English
Weight
426 KB
Volume
22
Category
Article
ISSN
0377-9017

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โœฆ Synopsis


We introduce the notion of a braided group. This is analogous to a supergroup with Bose-Fermi statistics __+ l replaced by braid statistics. We show that every algebraic quantum field theory in two dimensions leads to a braided group of internal symmetries. Every quantum group can be viewed as a braided group.


๐Ÿ“œ SIMILAR VOLUMES


Braided Groups and Quantum Fourier Trans
โœ V. Lyubashenko; S. Majid ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 908 KB

We show that acting on every finite-dimensional factorizable ribbon Hopf algebra \(H\) there are invertible operators \(\mathscr{S}_{-}, \mathscr{T}\) obeying the modular identities \(\left(\mathscr{S}_{-} \mathscr{T}\right)^{3}=\lambda \mathscr{P}^{2}\), where \(\lambda\) is a constant. The class i

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We consider quasitriangular Hopf algebras in braided tensor categories introduced by Majid. It is known that a quasitriangular Hopf algebra H in a braided monoidal category C induces a braiding in a full monoidal subcategory of the category of H-modules in C. Within this subcategory, a braided versi

Braids,q-Binomials, and Quantum Groups
โœ Marcelo Aguiar ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 414 KB

The classical identities between the q-binomial coefficients and factorials can be generalized to a context in which numbers are replaced by braids. More precisely, for every pair i, n of natural numbers, there is defined an element b ลฝ n. of the braid i group algebra kB , and these satisfy analogs