Winding-invariant prime ideals in quantum 3×3 matrices |
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Authors: | K R Goodearl T H Lenagan |
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Institution: | a Department of Mathematics, University of California, Santa Barbara, CA 93106, USA;b Department of Mathematics, JCMB, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, UK |
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Abstract: | A complete determination of the prime ideals invariant under winding automorphisms in the generic 3×3 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 3×3 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
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