Graded Skew Clifford Algebras That Are Twists of Graded Clifford Algebras
Graded Skew Clifford Algebras That Are Twists of Graded Clifford Algebras
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DOI：
10.1080/00927872.2013.847949
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发表时间：
2012-03
影响因子：
0.7
通讯作者：
Manizheh Nafari;M. Vancliff
中科院分区：
文献类型：
--
作者：
Manizheh Nafari;M. Vancliff
2010 年，Cassidy 和 Vancliff 提出了分级 Clifford 代数 (GCA) 的量化模拟，称为分级偏斜 Clifford 代数 (GSCA)，并且发现 GCA 的许多性质与 GSCA 具有对应的性质。特别是，GCA 是某个可交换子代数 C 上的有限模，而 GSCA 是（通常是非交换的）类似子代数 R 上的有限模。我们考虑常规 GSCA 是 GCA 通过自同构扭曲的情况，并且我们证明，在这种情况下，R 是斜多项式环，并且是 C 通过自同构扭曲。
In 2010, a quantized analog of a graded Clifford algebra (GCA), called a graded skew Clifford algebra (GSCA), was proposed by Cassidy and Vancliff, and many properties of GCAs were found to have counterparts for GSCAs. In particular, a GCA is a finite module over a certain commutative subalgebra C, while a GSCA is a finite module over a (typically noncommutative) analogous subalgebra R. We consider the case that a regular GSCA is a twist of a GCA by an automorphism, and we prove, in this case, R is a skew polynomial ring and a twist of C by an automorphism.