论文标题
关于$ q $ formed的Clifford代数的结构和表示理论
On the structure and representation theory of $q$-deformed Clifford algebras
论文作者
论文摘要
我们为Hayashi引入的量化Clifford代数提供了广义定义，使用了我们称之为扭曲的另一个参数$ k $。对于不等于$ 2 $的特征领域，我们为我们量化的Clifford代数提供了基础，表明它可以分解为等级$ 1 $ $ $ $ $ $ $，并计算其中心以表明它是一个经典的Clifford代数，这是订单订单组的订单组产品的组群体代数。此外，我们还表征了量子Clifford代数的半透明性，根据循环订单$ 2K $的半透明性，并提供一组不可约表示的表示。我们从量子群中构建形态，并解释经典和量子clifford代数之间的各种关系。通过更改发电机，我们提供了进一步的概括，以允许$ k $成为一个半整数，在这里我们恢复了Fadeev，Reshetikhin和Takhtajan引入的某些量子Clifford代数作为特殊情况。
We provide a generalized definition for the quantized Clifford algebra introduced by Hayashi using another parameter $k$ that we call the twist. For a field of characteristic not equal to $2$, we provide a basis for our quantized Clifford algebra, show that it can be decomposed into rank $1$ components, and compute its center to show it is a classical Clifford algebra over the group algebra of a product of cyclic groups of order $2k$. In addition, we characterize the semisimplicity of our quantum Clifford algebra in terms of the semisimplicity of a cyclic group of order $2k$ and give a complete set of irreducible representations. We construct morphisms from quantum groups and explain various relationships between the classical and quantum Clifford algebras. By changing our generators, we provide a further generalization to allow $k$ to be a half integer, where we recover certain quantum Clifford algebras introduced by Fadeev, Reshetikhin, and Takhtajan as a special case.
