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- W4310884107 abstract "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." @default.
- W4310884107 created "2022-12-20" @default.
- W4310884107 creator A5043588772 @default.
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- W4310884107 date "2022-12-06" @default.
- W4310884107 modified "2023-10-14" @default.
- W4310884107 title "On the structure and representation theory of $q$-deformed Clifford algebras" @default.
- W4310884107 doi "https://doi.org/10.48550/arxiv.2212.02925" @default.
- W4310884107 hasPublicationYear "2022" @default.
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