Abstract
AbstractLet $$(X,r_X)$$
(
X
,
r
X
)
and $$(Y,r_Y)$$
(
Y
,
r
Y
)
be finite nondegenerate involutive set-theoretic solutions of the Yang–Baxter equation, and let $$A_X = \mathcal {A}({{\textbf {k}}}, X, r_X)$$
A
X
=
A
(
k
,
X
,
r
X
)
and $$A_Y= \mathcal {A}({{\textbf {k}}}, Y, r_Y)$$
A
Y
=
A
(
k
,
Y
,
r
Y
)
be their quadratic Yang–Baxter algebras over a field $${{\textbf {k}}}$$
k
. We find an explicit presentation of the Segre product $$A_X\circ A_Y$$
A
X
∘
A
Y
in terms of one-generators and quadratic relations. We introduce analogues of Segre maps in the class of Yang–Baxter algebras and find their images and their kernels. The results agree with their classical analogues in the commutative case.
Funder
Max Planck Institute for Mathematics
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
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