RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Ufimsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 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)
References: PDF file   HTML file

Bibliographic databases:
UDC: 517.9

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}