Quantum hyperboloid and braided modules
نویسنده
چکیده
When a quantum hyperboloid is realized, as a three parameter algebra Ah,q, in the usual manner, the following problem arises: what is a ”representation theory” of this algebra? We construct the series of all spin representations of Ah,q, and we discuss a braided version of the orbit method, i.e. a correspondence between orbits in g∗ and g-modules. A braided trace and a braided involution are discussed as
منابع مشابه
Quantum Hyberboloid and Braided Modules
We construct a representation theory of a “quantum hyperboloid” in terms of so-called braided modules. We treat these objects in the framework of twisted Quantum Mechanics. Résumé Nous construisons une théorie de représentations pour « l’hyperboloïde quantique » en termes de modules tressés. Nous traitons ces objets dans le cadre de la mécanique quantique tordue.
متن کاملCrossed Modules and Quantum Groups in Braided Categories
Let A be a Hopf algebra in a braided category C. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category DY (C)AA of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group (A,A,R) the correspo...
متن کاملBraided modules and reflection equations
We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.
متن کاملMaxwell operator on q-Minkowski space and q-hyperboloid algebras
We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of ”quantum differential forms” as a projective module in the spirit of the Serre-Swan approach. Also, we use ”braided tangent vector fields” which are q-analogs of Poisson vector fields asso...
متن کاملBraided Geometry and the Inductive Construction of Lie Algebras and Quantum Groups
Double-bosonisation associates to a braided group in the category of modules of a quantum group, a new quantum group. We announce the semiclassical version of this inductive construction.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995