论文标题
量子组的度量兼容性和LEVI-CIVITA连接
Metric compatibility and Levi-Civita Connections on Quantum Groups
论文作者
论文摘要
研究了通用Hopf代数$ H $上的任意连接，并显示为张量字段上的连接。在此基础上，提出了公制兼容连接的一般定义。这导致了Levi-Civita连接的存在和独特性的足够标准，即$ h $值矩阵的可逆性。证明了所有与初始指标的指标，为所有指标的Levi-Civita连接的唯一性提供了不可逆转。该类别由既不是中心（双模图）也不是均衡的指标组成。对于中央和比科不变的指标，可逆条件进一步简化为指标独立的条件。示例包括$ sl_q（2）$的指标。
Arbitrary connections on a generic Hopf algebra $H$ are studied and shown to extend to connections on tensor fields. On this ground a general definition of metric compatible connection is proposed. This leads to a sufficient criterion for the existence and uniqueness of the Levi-Civita connection, that of invertibility of an $H$-valued matrix. Provided invertibility for one metric, existence and uniqueness of the Levi-Civita connection for all metrics conformal to the initial one is proven. This class consists of metrics which are neither central (bimodule maps) nor equivariant, in general. For central and bicoinvariant metrics the invertibility condition is further simplified to a metric independent one. Examples include metrics on $SL_q(2)$.
