Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primitive ideals and automorphisms of quantum matrices   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).

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn