Symplectic Groups, Quadratic Forms and Tensor Products of Quaternion Algebras
Speaker: Dr. Adam Chapman (Universite catholique de Louvain)
Time: 4.00PM
Date: Monday February 24th 2014
Location: CASL Seminar Room, Block 8, Belfield Office Park
Abstract:
We present a generating set for the symplectic group and conclude a chain equivalence for quadratic forms in characteristic 2. Using this chain equivalence, and the known chain equivalence for quadratic forms in characteristic not 2, we obtain a chain equivalence for tensor products of n quaternion algebras over of a field F satisfying the condition that if two 2n+2-dimensional quadratic forms q_1, q_2 in I_q^2(F) belong to the same congruence class in I_q^2(F)/I_q^3(F) then they are similar. This condition holds automatically if n=2 or if I_q^3(F)=0.
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