论文标题
量子二元性原理的量子连续kac-moody代数
Quantum Duality Principle for quantum continuous Kac-Moody algebras
论文作者
论文摘要
对于[A. Appel，F。Sala，“连续kac-moody代数的量化”，纯应用。数学。 Q. 16（2020），否。 3, 439-493], we prove that a suitable formulation of the Quantum Duality Principle holds true, both in a "formal" version - i.e., applying to the original definition of U_h(g_X) as a formal QUEA over the algebra of formal series in h - and in a "polynomial" one - i.e., for a suitable polynomial form of U_h(g_X) over the algebra of Laurent Q中的多项式。在这两种情况下，QDP都指出，lie bialgebra g_x给定量化的适当子代理实际上是连接的泊松型poisson g^*_ x dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual dual the Bialgebra g_x的适当量化。
For the quantized universal enveloping algebra U_h(g_X) associated with a continuous Kac-Moody algebra g_X as in [A. Appel, F. Sala, "Quantization of continuum Kac-Moody algebras", Pure Appl. Math. Q. 16 (2020), no. 3, 439-493], we prove that a suitable formulation of the Quantum Duality Principle holds true, both in a "formal" version - i.e., applying to the original definition of U_h(g_X) as a formal QUEA over the algebra of formal series in h - and in a "polynomial" one - i.e., for a suitable polynomial form of U_h(g_X) over the algebra of Laurent polynomials in q. In both cases, the QDP states that a suitable subalgebra of the given quantization of the Lie bialgebra g_X is in fact a suitable quantization (in formal or in polynomial sense) of a connected Poisson group G^*_X dual to g_X .
