On the parameterization of primitive ideals in affine PI algebras

Details On the parameterization of primitive ideals in affine PI algebras On the parameterization of primitive ideals in affine PI algebras

2005-05-26

arxiv.org/abs/math/0505556v3

Mathematics

Rings and Algebras

Improved; homeomorphism established for quantum groups at roots of unity. AMS-TeX 11 pages

Scientific paper

We consider the following question, concerning associative algebras R over an algebraically closed field k: When can the space of (equivalence classes of) finite dimensional irreducible representations of R be topologically embedded into a classical affine space? We provide an affirmative answer for algebraic quantum groups at roots of unity. More generally, we give an affirmative answer for k-affine maximal orders satisfying a polynomial identity, when k has characteristic zero. Our approach closely follows the foundational studies by Artin and Procesi on finite dimensional representations. Our results also depend on Procesi's later study of Cayley-Hamilton identities.

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