TECHNION FACULTY OF MATHEMATICS ALGEBRA SEMINAR SPEAKER: Jung-Miao Kuo, National Chung Hsing University, Taiwan TOPIC: A universality property of the Clifford algebras of ternary cubic forms 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. <http://www.technion.ac.il/~neftind/algebra_seminar.htm> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Jack Sonn <sonn@math.technion.ac.il>