Twist deformations of module homomorphisms and connections
Twist deformations of module homomorphisms and connections
复制标题
模块同态和连接的扭曲变形
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发表时间：
2012
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通讯作者：
Alexander Schenkel
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作者：
Alexander Schenkel
设H是一个Hopf代数，A是一个左H-模代数，V是一个左H-模A-双模.研究了V的右A-线性自同态在扭曲变形下的行为。特别地，我们构造了V_\星星的右A_\star-线性自同态的双射量子化映射，其中A_\星星，V_\星星表示A，V的通常扭曲变形.将量子化映射推广到左H-模A-双模之间的右A-线性同态和V上的右连通.给定一个拟三角Hopf代数，我们可以定义线性映射的H-协变张量积，它将左H-模A-双模限制为A上张量积模上的右A-线性同态的定义良好的张量积。这也需要代数和双模上的拟交换性条件。使用这个张量积，我们可以构造一个新的提升规定的连接到张量积模，推广通常的规定，也包括非等变连接。
Let H be a Hopf algebra, A a left H-module algebra and V a left H-module A-bimodule. We study the behavior of the right A-linear endomorphisms of V under twist deformation. We in particular construct a bijective quantization map to the right A_\star-linear endomorphisms of V_\star, with A_\star,V_\star denoting the usual twist deformations of A,V. The quantization map is extended to right A-linear homomorphisms between left H-module A-bimodules and to right connections on V. We then investigate the tensor product of linear maps between left H-modules. Given a quasitriangular Hopf algebra we can define an H-covariant tensor product of linear maps, which restricts for left H-module A-bimodules to a well-defined tensor product of right A-linear homomorphisms on tensor product modules over A. This also requires a quasi-commutativity condition on the algebra and bimodules. Using this tensor product we can construct a new lifting prescription of connections to tensor product modules, generalizing the usual prescription to also include nonequivariant connections.