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Notations: Let $Q=(a,b)$ be a quaternion algebra over a field of characteristic $\neq 2$, i.e. $i^2=a, j^2=b, k=ij, ij=-ji$. Consider $K=k(t)(\alpha)$, where $\alpha=\sqrt{at^2+b}$. Let $\sigma=Int(i)\...

I am currently reading Husemoller's wonderful book on fibre bundles, specifically the section on Clifford algebras. He defines these groups $L_k$ as follows. Let $M_k$ denote the free abelian groups ...

Page 205 of the book Classical Groups and Algebraic K-Theory defines a symplectic module to be an arbitrary quadratic module $(M,h,q)$ over a form ring $(R,\Lambda)$ with $(J,\varepsilon)$ where $J=\...

A somewhat elementary question but seemingly difficult to find a suitable reference: Consider the six-dimensional real space $\wedge^2(\mathbb R^4)$ with basis $e_i \wedge e_j \ (i < j)$ where $...

In the study of quadratic spaces over general rings, there is a type of scalar which people consider called a Form ring $(R,\Lambda)$ relative to some anti-automorphism denoted $(-)^J:R\to R$ and ...