New solutions of the Yang–Baxter equation with a square
R. A. Atnagulova, I. Z. Golubchik
Bashkir State Pedagogical University, Ufa, Russia
The paper is devoted to the Yang–Baxter equation with the square, that is, to the equation
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.
the Yang–Baxter equation with the square, integrable differential equations, complementary subalgebras in the algebra of Laurent series.
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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
\by R.~A.~Atnagulova, I.~Z.~Golubchik
\paper New solutions of the Yang--Baxter equation with a~square
\jour Ufimsk. Mat. Zh.
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