SPEAKER: Jung-Miao Kuo, National Chung Hsing University, Taiwan
TOPIC:  A universality property of the Clifford algebras of ternary cubic
DATE: Thursday, Jan 20, 2011
TIME: 12:30
PLACE: Amado 719
Abstract: In this talk, we introduce an algebra associated to a
cubic curve*C * defined over a field *F* of characteristic not
two or three. This algebra is Azumaya of rank 9 and its center
is the affine coordinate ring of an elliptic curve, namely the
Jacobian of the cubic curve *C*. The induced function from the
group of *F*-rational points on the Jacobian into the Brauer
group of *F *is a group homomorphism with image precisely the
relative Brauer group of classes of central simple *F*-algebras
split by the function field of *C*. Also, this algebra is split
if and only if the cubic curve *C *has an *F*-rational point.
Finally, we present a universality property of the family of
such algebras. These results generalize Haile's work on the
Clifford algebra of a binary cubic form.
Technion Math. Net (TECHMATH)
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