Vector generators of the real Clifford algebras
- Authors
- Song, Youngkwon; Lee, Doohann
- Issue Date
- Dec-2015
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- Clifford algebra; matrix representation; 15A66
- Citation
- LINEAR & MULTILINEAR ALGEBRA, v.63, no.12, pp.2448 - 2460
- Journal Title
- LINEAR & MULTILINEAR ALGEBRA
- Volume
- 63
- Number
- 12
- Start Page
- 2448
- End Page
- 2460
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/9807
- DOI
- 10.1080/03081087.2015.1018812
- ISSN
- 0308-1087
- Abstract
- In this paper, we introduce a method to obtain vector generators for the real matrix representation L p, q of the real Clifford algebra C l p, q from the real matrix representation L2n ( R) of C l 0, n with n = p+ q for every n. N. This can give a nice tool to classify the Clifford algebra C l p, q in the sense of generators. Also, we present the inverse of a nonzero vector in L2n ( R) and using the properties of vector generators in L p, q, we obtain some results about determinant and inverse of a vector in Ln- 1,1. Moreover, we show the relations of solutions for the linear equation xa = ax for some a. Delta in L0,2 and that for xb = bx in L p, q for some b. L p, q, where p + q = 2.
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