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HITZER, Eckhard
Senior Associate Professor Division of Arts and Sciences, College of Liberal Arts, International Christian University |
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| Language | English |
| Publication Date | 2011 |
| Type | Research Paper (Scientific Journal) |
| Peer Review | With peer review |
| Title | Geometric Roots of –1 in Clifford Algebras Cl(p,q) with p+q <= 4 |
| Contribution Type | Joint Work |
| Journal | Adv. In Appl. Cliff. Algebras |
| Journal Type | Another Country |
| Publisher | Birkhaeuser, Basel, Switzerland. |
| Volume, Issue, Pages | 21(1),pp.121-144 |
| Responsible for | Symbolic computations and most of text. |
| Author and coauthor | HITZER Eckhard, R. Abłamowicz |
| Details | 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 |