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7 votes
1 answer
633 views

Given a rational matrix $Q$, can we generate $\langle Q^{i}(v)\mid i\in\mathbb Z,v\in\mathbb Z^{2}\rangle$ using only non-negative powers of a matrix?

I have copied this question from StackExchange, thank you to those who helped me to improve the question. (apology if you have seen this question already) Let $Q $ be a matrix in $ \operatorname{GL}(...
5 votes
1 answer
271 views

Do all finite-dimensional division algebras appear as Wedderburn factors of rational group rings?

Suppose that $D$ is a division algebra that is finite-dimensional over $\Bbb Q$, does there exist a finite group $G$ such that one of the factors in the Wedderburn decomposition of $\Bbb Q[G]$ is a ...
2 votes
0 answers
142 views

calculation in a group ring

I have some problems with the verification of the third equation in Lemma 1 in this paper. First of all, one has to notice that there is at least one Error in the Definition of $a_{\kappa,\nu}$ above....