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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 3, Pages 6–16 (Mi ufa155)  

New solutions of the Yang–Baxter equation with a square

R. A. Atnagulova, I. Z. Golubchik

Bashkir State Pedagogical University, Ufa, Russia

Abstract: The paper is devoted to the Yang–Baxter equation with the square, that is, to the equation
$$ R([R(a),b]-[R(b),a])=R^2([a,b])+[R(a),R(b)], $$
where $a,b\in g$, $g$ – is a Lie algebra, and $R$ is a linear operator on the vector space $g$. Two series of operators $R$, satisfying this equation are constructed. In the construction we use Lie subalgebras in the matrix algebra, complementary to the subspace of matrices with zero last row.

Keywords: the Yang–Baxter equation with the square, integrable differential equations, complementary subalgebras in the algebra of Laurent series.

Full text: PDF file (428 kB)
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Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 19.12.2011

Citation: R. A. Atnagulova, I. Z. Golubchik, “New solutions of the Yang–Baxter equation with a square”, Ufimsk. Mat. Zh., 4:3 (2012), 6–16

Citation in format AMSBIB
\Bibitem{AtnGol12}
\by R.~A.~Atnagulova, I.~Z.~Golubchik
\paper New solutions of the Yang--Baxter equation with a~square
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 3
\pages 6--16
\mathnet{http://mi.mathnet.ru/ufa155}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429919}


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