caa a22 4500 47709483X CHVBK 20180405111524.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF03322196 doi (NATIONALLICENCE)springer-10.1007/BF03322196 Normed Bilinear Pairings for Semi-Euclidean Spaces near the Hurwitz-Radon Range [Elektronische Daten] [Hillel Gauchman, Gabor Toth] A codimension c(≥ 0) orthogonal multiplication of type (k,l;m;m+ c) for semi-Euclidean spaces is a normed bilinear map F: Rk,l × Rm → Rm+C, k + l ≤ m, k > 0, where the signatures of the semi-Euclidean spaces Rm and Rm+C are suppressed. For the Hurwitz-Radon range, i.e. c = 0, F gives rise to (and is determined by) a module over the Clifford algebra C l,k- 1 whose generators possess certain invariance properties with respect to the semi-Euclidean structure on the module. For c = 1, we prove an Adem-type restriction-extension theorem to the effect that F (up to isometries on the source and the range) restricts to an orthogonal multiplication of type (k, l; m; m) if m is even, and extends to an orthogonal multiplication of type (k, l; m + 1; m + 1) if m is odd. The resulting types are in the Hurwitz-Radon range, thereby classified. The main results of the paper give a full description of codimension two full orthogonal multiplications F of type (k, l; m; m + 2). We show that, for m even, F extends to an orthogonal multiplication of type (k, l; m + 2; m + 2). For m odd, we have k + l = 3 and F restricts (again up to isometries on the source and the range) to an orthogonal multiplication of type (k, l; m — 1; m — 1) which is a direct summand of F. AMS Subject Classification: Primary 15A63, Secondary 11E25. Birkhäuser Verlag, Basel, 1996 Orthogonal multiplication nationallicence Clifford module nationallicence semi-Euclidean space nationallicence Gauchman Hillel University of Illinois at Urbana-Champaign, IL 61920, USA aut Toth Gabor Rutgers University, NJ 08102, Camden, USA aut Results in Mathematics Birkhäuser-Verlag 30/3-4(1996-11-01), 276-301 0378-6218 30:3-4<276 1996 30 25 https://doi.org/10.1007/BF03322196 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF03322196 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gauchman Hillel University of Illinois at Urbana-Champaign, IL 61920, USA aut NATIONALLICENCE 700 1- Toth Gabor Rutgers University, NJ 08102, Camden, USA aut NATIONALLICENCE 773 0- Results in Mathematics Birkhäuser-Verlag 30/3-4(1996-11-01), 276-301 0378-6218 30:3-4<276 1996 30 25 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer