Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Centralizing traces and Lie triple isomorphisms on generalized matrix
  algebras   Let $\mathcal{G}$ be a generalized matrix algebra over a commutative ring
$\mathcal{R}$ and $\mathcal{Z(G)}$ be the center of $\mathcal{G}$. Suppose that
${\mathfrak q}\colon \mathcal{G}\times \mathcal{G}\longrightarrow \mathcal{G}$
is an $\mathcal{R}$-bilinear mapping and ${\mathfrak T}_{\mathfrak q}\colon
\mathcal{G}\longrightarrow \mathcal{G}$ is the trace of $\mathfrak{q}$. We
describe the form of ${\mathfrak T}_{\mathfrak q}$ satisfying the condition
$[{\mathfrak T}_{\mathfrak q}(G), G]\in \mathcal{Z(G)}$ for all $G\in
\mathcal{G}$. The question of when ${\mathfrak T}_{\mathfrak q}$ has the proper
form is considered. Using the aforementioned trace function, we establish
sufficient conditions for each Lie triple isomorphism of $\mathcal{G}$ to be
almost standard. As applications we characterize Lie triple isomorphisms of
full matrix algebras, of triangular algebras and of certain unital algebras
with nontrivial idempotents. Some topics for future research closely related to
our current work are proposed at the end of this article.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an