M ay 2 00 1 Quantum solvable algebras . Ideals and representations at roots of 1
نویسنده
چکیده
There proved that every prime invariant with respect to quantum adjoint action ideal I is completely prime and Fract(R/I) is isomorphic to the skew field of fractions of an algebra of twisted polynomials. We study correspondence between symplectic leaves and irreducible representations. The Conjecture of De Concini-KacProcesi on dimension of irreducible representations is proved for sufficiently great l.
منابع مشابه
Stratification of prime spectrum of quantum solvable algebras
1 Introduction. We consider the class of Noetherian ring, appeared as a result of quantization of algebraic groups and their representations within framework of mathematical physics. One set up the problem of description of prime and primitive spectrum of these rings. This problem has been solved first for algebras of low dimension , then for the case GL q (n), later for general case of regular...
متن کاملIrreducible Representations of Quantum Solvable Algebras at Roots of 1
The relationship between the irreducible representations of quantum solvable algebras at roots of 1 and the points of the variety of the center is studied. The quiver of the fiber algebra is characterized, and formulas for the dimension and for the number of the irreducible representations that lie over a point of the center variety are presented.
متن کاملar X iv : m at h / 03 05 34 2 v 1 [ m at h . O A ] 2 6 M ay 2 00 3 State spaces of JB ∗ - triples ∗ Matthew
An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a JB∗-triple, and up to complete isometry, of one-sided ideals in C∗-algebras.
متن کاملM ay 2 00 2 POISSON ORDERS , SYMPLECTIC REFLECTION ALGEBRAS AND REPRESENTATION THEORY
We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in positive characteristic. Quite generally, we study this class of algebras from the point of view of Poisson geometry, exhibiting connections between their represent...
متن کاملar X iv : m at h / 03 05 30 9 v 1 [ m at h . Q A ] 2 2 M ay 2 00 3 Representations of cross product algebras of Podles ’ quantum spheres
Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podles’ spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hop...
متن کامل