Launois, Stephane, 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) (KAR id:2167)
PDF (Primitive Ideals and Automorphisms)
Language: English 

Download this file (PDF/342kB) 
Preview 
Request a format suitable for use with assistive technology e.g. a screenreader  
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 

DOI/Identification number:  10.1007/s1046800790590 
Uncontrolled keywords:  quantum matrices; quantum minors; prime ideals; primitive ideals; automorphisms 
Subjects:  Q Science > QA Mathematics (inc Computing science) 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Anna Thomas4 
Date Deposited:  19 Dec 2007 19:31 UTC 
Last Modified:  16 Nov 2021 09:40 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/2167 (The current URI for this page, for reference purposes) 
 Link to SensusAccess
 Export to:
 RefWorks
 EPrints3 XML
 BibTeX
 CSV
 Depositors only (login required):