ヒッツェル，エクハルト   HITZER, Eckhard   ヒッツェル, エクハルト    所属   国際基督教大学教養学部 アーツ・サイエンス学科    職種   上級准教授
言語種別	英語
発行・発表の年月	2011
形態種別	研究論文（学術雑誌）
査読	査読あり
標題	Geometric Roots of –1 in Clifford Algebras Cl(p,q) with p+q <= 4
執筆形態	共著
掲載誌名	Adv. In Appl. Cliff. Algebras
掲載区分	国外
出版社・発行元	Birkhaeuser, Basel, Switzerland.
巻・号・頁	21(1),pp.121-144
担当範囲	Symbolic computations and most of text.
著者・共著者	HITZER Eckhard, R. Abłamowicz
概要	It is known that Clifford (geometric) algebra offers a geometric interpretation for square roots of -1 in the form of blades that square to minus 1. This extends to a geometric interpretation of quaternions as the side face bivectors of a unit cube. Research has been done [S. J. Sangwine, Biquaternion (Complexified Quaternion) Roots of -1, Adv. Appl. Cliford Alg. 16(1), pp. 63-68, 2006.] on the biquaternion roots of -1, abandoning the restriction to blades. Biquaternions are isomorphic to the Clifford (geometric) algebra C(3,0) of R^3. All these roots of -1 find immediate applications in the construction of new types of geometric Clifford Fourier transformations. We now extend this research to general algebras C(p,q). We fully derive the geometric roots of -1 for the Clifford (geometric) algebras with p+q <= 4.
DOI	10.1007/s00006-010-0240-x