Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hattori-Stallings trace and character   It is shown that Hattori-Stallings trace induces a homomorphism of abelian
groups, called Hattori-Stallings character, from the $K_1$-group of
endomorphisms of the perfect derived category of an algebra to its zero-th
Hochschild homology, which provides a new proof of Igusa-Liu-Paquette Theorem,
i.e., the strong no loop conjecture for finite-dimensional elementary algebras,
on the level of complexes. Moreover, the Hattori-Stallings traces of projective
bimodules and one-sided projective bimodules are studied, which provides
another proof of Igusa-Liu-Paquette Theorem on the level of modules.

5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex