Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong shift equivalence and algebraic K-theory   Let R be a ring. Let SSE-R be the equivalence relation on square matrices
(allowed to have different size) over R generated by A ~ B if there exist
matrices U,V over R such that A = UV and B = VU . An invariant of SSE-R is
shift equivalence over R (SE-R); for example, A and B are SE-R iff the
R[t]-modules cok(I-tA) and cok(I-tB) are isomorphic. We show that the
refinement of SE-R by SSE-R is captured precisely by NK_1(R)/E(A,R), where the
"elementary stabilizer" group E(A,R) depends on the SE-R class of A. E(A,R) is
trivial if A is invertible, and in some related cases; for general R, our proof
of this relies on the K-theory of noncommutative localization developed by
Neeman and Ranicki. The result has application to symbolic dynamics. For R
commutative, the union over A of the E(A,R) equals NSK_1(R); the proof uses a
stabilization result of Fitting and (especially) the Nenashev characterization
of K_1 of an exact category, applied to the exact category of f.g. modules over
R[t] with a projective resolution of length at most 1.

36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th