Skew Clifford algebras |
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Authors: | Thomas Cassidy Michaela Vancliff |
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Institution: | 1. Mathematics Department, Bucknell University, Lewisburg, PA 17837, USA;2. Department of Mathematics, Box 19408, University of Texas at Arlington, Arlington, TX 76019-0408, USA |
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Abstract: | We introduce a generalization, called a skew Clifford algebra, of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined in 2010. In particular, we examine homogenizations of skew Clifford algebras, and determine which skew Clifford algebras can be homogenized to create Artin-Schelter regular algebras. Just as (classical) Clifford algebras are the Poincaré-Birkhoff-Witt (PBW) deformations of exterior algebras, skew Clifford algebras are the -graded PBW deformations of quantum exterior algebras. We also determine the possible dimensions of skew Clifford algebras and provide several examples. |
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Keywords: | Corresponding author 16S10 16W55 16S20 Clifford algebra Regular algebra Deformation Homogenization Quadratic algebra Quadratic form |
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