Let $k$ be a field, assumed to have characteristic $0$ for simplicity (though this probably isn't necessary). Let $A$ be a central simple algebra over $k$ of dimension $n^2$. The …

Let $F$ be a field of characteristic $\neq 2$. Suppose $(A,\sigma)$ is a finite dimensional central simple algebra over a field $F$ with an orthogonal involution. Assume (A,σ) is n …

Suppose $D$ is an explicitly given rank 9 central simple algebra over ${\mathbb Q}$ (or a number field). For example it could be specified by two cubic subfields ${\mathbb Q}(a), { …

Let $k$ be a field which I don't suppose to be algebraically closed. Then, the endomorphism ring of any irreducible representation of a finite group over $k$ is a division ring. W …

As noted earlier, I found reading Weil's book "Basic Number Theory" to be a harrowing experience, and I find his writing to be intrinsically hard to understand, though it is perfec …

This is really an irrelevant question in the sense that the answer isn't remotely "logically crucial for the Langlands programme" or whatever---it's just something that occurred to …

In this question F is a field and all algebras are finite dimensional F algebras. Let X be the set of all F algebras A for which there exist an F algebra B and an F division alge …

Let $E/F$ be a quadratic extension of $p$-adic fields. Consider $M_n(E)$ with the unitary (aka 2nd kind) involution $X \mapsto \sigma(X)^{tr}$, where $\sigma(X)$ denotes the entry- …