Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reflection equation as a tool for studying solutions to the Yang-Baxter
  equation   Given a right-non-degenerate set-theoretic solution $(X,r)$ to the
Yang-Baxter equation, we construct a whole family of YBE solutions $r^{(k)}$ on
$X$ indexed by its reflections $k$ (i.e., solutions to the reflection equation
for $r$). This family includes the original solution and the classical derived
solution. All these solutions induce isomorphic actions of the braid
group/monoid on $X^n$. The structure monoids of $r$ and $r^{(k)}$ are related
by an explicit bijective $1$-cocycle-like map. We thus turn reflections into a
tool for studying YBE solutions, rather than a side object of study. In a
different direction, we study the reflection equation for non-degenerate
involutive YBE solutions, show it to be equivalent to (any of the) three
simpler relations, and deduce from the latter systematic ways of constructing
new reflections.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin