Primitive ideals and automorphisms of quantum matrices
| dc.creator | Launois, S | |
| dc.creator | Lenagan, T H | |
| dc.date | 2005-11-16 | |
| dc.date.accessioned | 2026-07-07T06:51:20Z | |
| dc.date.available | 2026-07-07T06:51:20Z | |
| dc.description | Let q be a nonzero complex number that is not a root of unity. We give a criterion for (0) to be a primitive ideal of the algebra O_q(M_{m,n}) of quantum matrices. Next, we describe all height one primes of O_q(M_{m,n}); these two problems are actually interlinked since it turns out that (0) is a primitive ideal of O_q(M_{m,n}) whenever O_q(M_{m,n}) has only finitely many height one primes. Finally, we compute the automorphism group of O_q(M_{m,n}) in the case where m is not equal to n. In order to do this, we first study the action of this group on the prime spectrum of O_q(M_{m,n}). Then, by using the preferred basis of O_q(M_{m,n}) and PBW bases, we prove that the automorphism group of O_q(M_{m,n}) is isomorphic to the torus (C*)^{m+n-1} when m is not equal to n, and (m,n) is not equal to (1,3) and (3,1). | |
| dc.identifier | https://arxiv.org/abs/math/0511409 | |
| dc.identifier | http://arxiv.org/abs/math/0511409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104950 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W35; 16W20; 20G42; 81R50 | |
| dc.title | Primitive ideals and automorphisms of quantum matrices | |
| dc.type | text |