论文标题
在不可还原量子标志歧管上的相对线模块的双模块连接
Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds
论文作者
论文摘要
最近（第二作者和迪亚兹·加西亚（DíazGarcía），克鲁托夫（Krutov），桑伯格（Somberg）和斯特朗（Strung）表明，每个相对线模块上的每个相对线模块都无法可减少量子标志歧管$ \ mathcal {o} _q（g/l_s）$接纳一个独特的$ \ mathcal {o} _q（g）_q（g）$ - col-corvariant Carcirber sidge the hecken hecken heck hecken的唯一$ \ mathcal {o} _q（g/l_s） $ω^1_Q（g/l_s）$。在本文中，我们表明这些连接是带有可逆相关的双模块图的双模模型连接。通过将Beggs和Majid的一般结果以及量子主束的主要连接应用于最近由作者和DíazGarcía最近构建的Heckenberger-Kolb calculi的量子捆绑包中的主要连接证明。首先以广义量子决定因素的方式给出了相关的双模图的明确介绍，然后根据代数$ \ Mathcal {O} _Q（g）$的frt表示，最后就Takeuchi的类别等价而言。
It was recently shown (by the second author and Díaz García, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold $\mathcal{O}_q(G/L_S)$ admits a unique $\mathcal{O}_q(G)$-covariant connection with respect to the Heckenberger-Kolb differential calculus $Ω^1_q(G/L_S)$. In this paper we show that these connections are bimodule connections with an invertible associated bimodule map. This is proved by applying general results of Beggs and Majid, on principal connections for quantum principal bundles, to the quantum principal bundle presentation of the Heckenberger-Kolb calculi recently constructed by the authors and Díaz García. Explicit presentations of the associated bimodule maps are given first in terms of generalised quantum determinants, then in terms of the FRT presentation of the algebra $\mathcal{O}_q(G)$, and finally in terms of Takeuchi's categorical equivalence for relative Hopf modules.
