On abelian group actions and Galois quantizations

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• 作者：H.L. Huru^a ; ^{hilja.huru@hifm.no} ; V.V. Lychagin^b ; ^{valentin.lychagin@uit.no}
• 关键词：Categorical quantizations ; Galois extensions ; Clifford algebras
• 刊名：Journal of Geometry and Physics
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：70
• 期：Complete
• 页码：81-97
• 全文大小：456 K

文摘

Quantizations of actions of finite abelian groups are explicitly described by elements in the tensor square of the group algebra of . Over algebraically closed fields of characteristic 0 these are in one to one correspondence with the second cohomology group of the dual of . With certain adjustments this result is applied to group actions over any field of characteristic 0. In particular we consider the quantizations of Galois extensions, which are quantized by ¡°deforming¡± the multiplication. For the splitting fields of products of quadratic polynomials this produces quantized Galois extensions that all are Clifford type algebras.