The conventional d-dimensional fermion algebra does not have a Hopf algebra structure. It is shown that this algebra can be deformed by introducing angular elements and by combining the commutative sine-cosine algebra with the Clifford algebra so that the resulting d-dimensional fermion algebra is a Hopf algebra.

中文翻译：

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θ变形的多维费米子代数

常规的d维费米子代数不具有霍夫夫代数结构。结果表明，该代数可以通过引入角元素并将可交换的正弦余弦代数与Clifford代数相结合而变形，从而使所得的d维费米子代数为Hopf代数。