Launois, Stephane and Lenagan, T.H. (2007) Primitive ideals and automorphisms of quantum matrices. Algebras and Representation Theory, 10 (4). pp. 339365. ISSN 1386923X. (doi:10.1007/s1046800790590) (Full text available)
PDF (Primitive Ideals and Automorphisms)  
Download (332kB)



Official URL http://dx.doi.org/10.1007/s1046800790590 
Abstract
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 Oq(Mm,Mn) 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 Oq(Mm,Mn) whenever Oq(Mm,Mn) has only finitely many height one primes. Finally, we compute the automorphism group of Oq(Mm,Mn) 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 Oq(Mm,Mn). Then, by using the preferred basis of Oq(Mm,Mn) and PBW bases, we prove that the automorphism group of Oq(Mm,Mn) is isomorphic to the torus (K*)(m+n=1) when m not equal n and (m, n) not equal (1, 3) (3, 1).
Item Type:  Article 

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 Thomas4 
Date Deposited:  19 Dec 2007 19:31 
Last Modified:  28 May 2014 10:56 
Resource URI:  https://kar.kent.ac.uk/id/eprint/2167 (The current URI for this page, for reference purposes) 
 Export to:
 RefWorks
 EPrints3 XML
 BibTeX
 CSV
 Depositors only (login required):
Downloads
Downloads per month over past year