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 2013 形態種別 研究論文（国際会議プロシーディングス） 査読 査読あり 標題 Square roots of -1 in real Clifford algebras 執筆形態 共著 掲載誌名 Trends in Mathematics, Vol 27, Birkhauser, Basel, 2013. 巻・号・頁 pp.123-153 著者・共著者 HITZER Eckhard, J. Helmstetter, R. Ablamowicz 概要 Let Cl(p,q) be the universal Clifford algebra (associative with unit) generated over R by p + q elements e_k (with k = 1, 2, ... , p + q) with the relations e^2_k = 1 if k <= p, e^2_k = -1 if k > p and e_he_k + e_ke_h = 0 whenever h not equal k, see [6]. We set n = p + q and s = p - q. This algebra has dimension 2^n, and its even subalgebra Cl_0(p,q) has dimension 2^{n-1} (if n > 0). We are concerned with square roots of -1 contained in Cl(p,q) or Cl_0(p,q). If the dimension of Cl(p,q) or C_0(p,q) is less or equal 2, it is isomorphic to R or R^2 or C, and it is clear that there is no square root of -1 in R and R2 = R x R, and that there are two squares roots i and -i in C. Therefore we only consider algebras of dimension greater or equal 4. Square roots of -1 have been computed in [4] for algebras of dimension less or equal 16, and for Cl(3,0) in [7]. DOI 10.1007/978-3-0348-0603-9_7