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Jordan pairs of quadratic forms are generalized so that they have forms with values in invertible modules. The role of such pairs turns out to be natural in describing 'big cells', a kind of open charts around unit sections, of Clifford and orthogonal groups as group schemes. Group germ structures on big cells are particularly interested in and related also to Cayley-Lipschitz transforms.
Ikai, Hisatoshi. "Jordan pairs of quadratic forms with values in invertible modules.." Collectanea Mathematica 58.1 (2007): 85-100. <http://eudml.org/doc/41798>.
@article{Ikai2007, abstract = {Jordan pairs of quadratic forms are generalized so that they have forms with values in invertible modules. The role of such pairs turns out to be natural in describing 'big cells', a kind of open charts around unit sections, of Clifford and orthogonal groups as group schemes. Group germ structures on big cells are particularly interested in and related also to Cayley-Lipschitz transforms.}, author = {Ikai, Hisatoshi}, journal = {Collectanea Mathematica}, keywords = {Algebras de Jordan; Formas cuadráticas; Módulos algebraicos; big cell; Jordan pair; Clifford group; orthogonal group}, language = {eng}, number = {1}, pages = {85-100}, title = {Jordan pairs of quadratic forms with values in invertible modules.}, url = {http://eudml.org/doc/41798}, volume = {58}, year = {2007}, }
TY - JOUR AU - Ikai, Hisatoshi TI - Jordan pairs of quadratic forms with values in invertible modules. JO - Collectanea Mathematica PY - 2007 VL - 58 IS - 1 SP - 85 EP - 100 AB - Jordan pairs of quadratic forms are generalized so that they have forms with values in invertible modules. The role of such pairs turns out to be natural in describing 'big cells', a kind of open charts around unit sections, of Clifford and orthogonal groups as group schemes. Group germ structures on big cells are particularly interested in and related also to Cayley-Lipschitz transforms. LA - eng KW - Algebras de Jordan; Formas cuadráticas; Módulos algebraicos; big cell; Jordan pair; Clifford group; orthogonal group UR - http://eudml.org/doc/41798 ER -