Publications (3)0 Total impact
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ABSTRACT: The extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ is
quantized from three different points of view in this paper, which produces
three noncommutative and noncocommutative Hopf algebra structures, and yield
other three quantizations by an isomorphism of
$\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ correspondingly. Moreover, two of these
quantizations can be restricted to the extended affine Lie algebra
${sl_2(\mathbb{C}_q)}$.
11/2011;
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ABSTRACT: In the present paper we shall investigate the Lie bialgebra structures on the
Lie algebra $\widetilde{\frak{sl}_2(C_q[x,y])}$, which are shown to be
triangular coboundary.
02/2011;
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ABSTRACT: Lie bialgebra structures on the extended affine Lie algebra
$\widetilde{sl_2(\mathbb{C}_q)}$ are investigated. In particular, all Lie
bialgebra structures on $\widetilde{sl_2(\mathbb{C}_q)}$ are shown to be
triangular coboundary. This result is obtained by employing some techniques,
which may also work for more general extended affine Lie algebras, to prove the
triviality of the first cohomology group of $\widetilde{sl_2(\mathbb{C}_q)}$
with coefficients in the tensor product of its adjoint module, namely,
$H^1(\widetilde{sl_2(\mathbb{C}_q)},\widetilde{sl_2(\mathbb{C}_q)}\otimes\widetilde{sl_2(\mathbb{C}_q)})=0$.
02/2011;
