Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Veronese subalgebras and Veronese morphisms for a class of Yang-Baxter
  algebras   We study $d$-Veronese subalgebras $A^{(d)}$ of quadratic algebras $A_X= A(K,
X, r)$ related to finite nondegenerate involutive set-theoretic solutions $(X,
r)$ of the Yang-Baxter equation, where $K$ is a field and $d\geq 2$ is an
integer. We find an explicit presentation of the $d$-Veronese $A^{(d)}$ in
terms of one-generators and quadratic relations. We introduce the notion of a
$d$-Veronese solution $(Y, r_Y)$, canonically associated to $(X,r)$ and use its
Yang-Baxter algebra $A_Y= A(K, Y, r_Y)$ to define a Veronese morphism
$v_{n,d}:A_Y \rightarrow A_X $. We prove that the image of $v_{n,d}$ is the
$d$-Veronese subalgebra $A^{(d)}$, and find explicitly a minimal set of
generators for its kernel. The results agree with their classical analogues in
the commutative case, which corresponds to the case when $(X,r)$ is the trivial
solution.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph