Displaying similar documents to “Arithmetic of Hermitian forms.”

Applications of spinor class fields: embeddings of orders and quaternionic lattices

Luis Arenas-Carmona (2003)

Annales de l'Institut Fourier

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We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.

On the cokernel of the Witt decomposition map

Gabriele Nebe (2000)

Journal de théorie des nombres de Bordeaux

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Let R be a Dedekind domain with field of fractions K and G a finite group. We show that, if R is a ring of p -adic integers, then the Witt decomposition map δ between the Grothendieck-Witt group of bilinear K G -modules and the one of finite bilinear R G -modules is surjective. For number fields K , δ is also surjective, if G is a nilpotent group of odd order, but there are counterexamples for groups of even order.

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)

Open Mathematics

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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....