Decomposition of Involutions on Inertially Split Division Algebras
نویسندگان
چکیده
Let F be a Henselian valued field with char(F ) 6= 2, and let S be an inertially split F -central division algebra with involution σ∗ that is trivial on an inertial lift in S of the field Z(S). We prove necessary and sufficient conditions for S to contain a σ∗stable quaternion F -subalgebra, and for (S, σ∗) to decompose into a tensor product of quaternion algebras. These conditions are in terms of decomposability of an associated residue central simple algebra I that arises from a Brauer group decomposition of S.
منابع مشابه
Algebras and Involutions
• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...
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