General twisting of algebras
General twisting of algebras
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DOI：
10.1016/j.aim.2006.10.003
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发表时间：
2006-05
影响因子：
1.7
通讯作者：
J. L. Peña;F. Panaite;F. Oystaeyen
中科院分区：
文献类型：
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作者：
J. L. Peña;F. Panaite;F. Oystaeyen
对于么半群范畴中的代数(A，μ，u)，我们引入了伪扭子的概念(在特殊情况下称为缠绕和辫子缠绕)，作为态射T：A⊗A→A⊗A满足一列公理，保证了(A，μ0T，u)也是范畴中的代数.这一概念为各种变形(或扭曲)代数提供了一个统一的框架，如代数的扭曲张量积、扭曲双代数和具有Fedosov积的代数。伪扭曲也出现在文献中的其他主题中，例如达德维奇的辫子量子群和带状代数。我们还着重讨论了绞线对普适一阶微积分的影响，以及普适微分形式代数中绞线到编织绞线的升降问题。
We introduce the concept of pseudotwistor (with particular cases called twistor and braided twistor) for an algebra (A,μ,u) in a monoidal category, as a morphism T:A⊗A→A⊗A satisfying a list of axioms ensuring that (A,μ○T,u) is also an algebra in the category. This concept provides a unifying framework for various deformed (or twisted) algebras from the literature, such as twisted tensor products of algebras, twisted bialgebras and algebras endowed with Fedosov products. Pseudotwistors appear also in other topics from the literature, e.g. Durdevich's braided quantum groups and ribbon algebras. We also focus on the effect of twistors on the universal first order differential calculus, as well as on lifting twistors to braided twistors on the algebra of universal differential forms.