Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories
Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories
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DOI：
10.1007/s11005-010-0412-6
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发表时间：
2009-06
影响因子：
1.2
通讯作者：
P. Baseilhac;S. Belliard
中科院分区：
文献类型：
--
作者：
P. Baseilhac;S. Belliard
介绍并研究了q- onsager代数的推广。在q= 1的最简单情况下，代数简化为Uglov-Ivanov提出的代数。在q≠1的一般情况下，给出了量子仿射李代数（简和非简带）的共理想子代数的显代数同态。然后根据这些结果考虑了边界（非保持孤子）可积量子Toda场论。第一次明确地得到了底层非阿贝尔对称代数的所有定义关系。因此，基于纯代数参数，对所有可积（固定或动态）边界条件进行了分类。
Generalizations of theq-Onsager algebra are introduced and studied. In one of the simplest case andq= 1, the algebra reduces to the one proposed by Uglov–Ivanov. In the general case andq≠ 1, an explicit algebra homomorphism associated with coideal subalgebras of quantum affine Lie algebras (simply and non-simply laced) is exhibited. Boundary (soliton non-preserving) integrable quantum Toda field theories are then considered in light of these results. For the first time, all defining relations for the underlying non-Abelian symmetry algebra are explicitly obtained. As a consequence, based on purely algebraic arguments all integrable (fixed or dynamical) boundary conditions are classified.