Winding-invariant prime ideals in quantum 3×3 matrices

✍ Scribed by K.R. Goodearl; T.H. Lenagan

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 379 KB
• Volume: 260
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00566-5

✦ Synopsis

A complete determination of the prime ideals invariant under winding automorphisms in the generic 3 × 3 quantum matrix algebra O q (M 3 (k)) 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 O q (M n (k)).