Launois, S. and Lenagan, T.H. (2007) Primitive ideals and automorphisms of quantum matrices. Algebras and Representation Theory, 10 (4). pp. 339-365. ISSN 1386-923X.
|PDF (Primitive Ideals and Automorphisms)|
Let K be a field and q be a nonzero element of K 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,M-n) of quantum matrices. Next, we describe all height one primes of these two problems are actually interlinked since it turns out that (0) is a primitive ideal of O-q(M-m,M-n) whenever O-q(M-m,M-n) has only finitely many height one primes. Finally, we compute the automorphism group of O-q(M-m,M-n) in the case where m not equal n. In order to do this, we first study the action of this group on the prime spectrum of O-q(M-m,M-n). Then, by using the preferred basis of O-q(M-m,M-n) and PBW bases, we prove that the automorphism group of O-q(M-m,M-n) is isomorphic to the torus (K*)(m+n=1) when m not equal n and (m, n) not equal (1, 3) (3, 1).
|Uncontrolled keywords:||quantum matrices; quantum minors; prime ideals; primitive ideals; automorphisms|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Anna Thomas-4|
|Date Deposited:||19 Dec 2007 19:31|
|Last Modified:||05 Sep 2011 23:26|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/2167 (The current URI for this page, for reference purposes)|
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