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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
15
votes
Accepted
Explanation for $\chi(\operatorname{SL}_2(\mathbb{Z})) = -1/12$ with zeta function
(Expanding my comment into an answer)
It is not a coincidence. Relating the Euler characteristic of certain arithmetic groups to the Zeta function is a theorem due to Harder [1] from 1971. It is expan …
2
votes
Is there a CAS that can solve a given system of equations in a finite group algebra $kG$?
As you say you have a given system of equations, you can do this by brute-force in GAP. The following constructs a group algebra $kG$ in GAP -- this one constructs $kG$ when $k = GF(4)$ and $G = C_2$. …