Winding-invariant prime ideals in quantum $3\times3$ matrices

Details Winding-invariant prime ideals in quantum $3\times3$ matrices Winding-invariant prime ideals in quantum $3\times3$ matrices

2001-12-05

arxiv.org/abs/math/0112051v1

Mathematics

Quantum Algebra

29 pages; one eps figure. Fully integrated version at http://www.math.ucsb.edu/~goodearl/preprints.html/

Scientific paper

A complete determination of the prime ideals invariant under winding automorphisms in the generic 3 by 3 quantum matrix algebra is obtained. Explicit generating sets consisting of quantum minors are given for all of these primes, thus verifying a general conjecture in the 3 by 3 case. The result relies heavily on certain tensor product decompositions for winding-invariant prime ideals, developed in an accompanying paper. In addition, new methods are developed here, which show that certain sets of quantum minors, not previously manageable, generate prime ideals in the n by n quantum matrix algebra.

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