Tensor product decompositions of the real clifford algebra
- Authors
- Song, Y.; Lee, D.
- Issue Date
- Sep-2015
- Publisher
- Pushpa Publishing House
- Keywords
- Clifford algebra; Matrix representation
- Citation
- Far East Journal of Mathematical Sciences, v.98, no.1, pp.119 - 131
- Journal Title
- Far East Journal of Mathematical Sciences
- Volume
- 98
- Number
- 1
- Start Page
- 119
- End Page
- 131
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/10976
- DOI
- 10.17654/FJMSSep2015_119_131
- ISSN
- 0972-0871
- Abstract
- In this paper, we present some methods to decompose the Clifford algebra Cl<inf>p,q</inf> into some Clifford algebras via tensor product by using the vector generators of Cl<inf>0, p</inf>, Cl<inf>0,q</inf> and Cl<inf>p,0</inf> In particular, we prove that Cl<inf>n−k+1,k−1</inf> is isomorphic to Cl<inf>0,n k+1</inf> ⊗ Cl<inf>0,k−1</inf> if k −1= 2t for some odd number t and Cl<inf>n−k+1,k−1</inf> is isomorphic to Cl<inf>n-k+1, 0</inf> ⊗ CA0, k−1 if k − 1 = 2t for some even number t. Furthermore, we apply those results to matrix representations of the real Clifford algebras.a. © 2015 Pushpa Publishing House, Allahabad, India.
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