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10 votes
0 answers
194 views

Singularity category of a hypersurface associated to $M_{11}$

For reasons to do with classifying spaces of finite groups, I have the following algebra. Let $k$ be a field of characteristic two, and let $R = k[x,y,z]/(x^2 y + z^2)$, as a graded $k$-algebra with $|...
4 votes
1 answer
382 views

Non-existence of projective covers

I didn't get the argument of Example 7.3.11, page 123, from the representation theory book of Peter Webb, available also online at: http://www-users.math.umn.edu/~webb/RepBook/RepBookLatex.pdf In ...
4 votes
1 answer
343 views

Why do Nakajima and Watanabe claim the induced action of a finite linear group on the invariant subring of the reflection subgroup is linearizable?

I just picked up the paper "The classification of quotient singularities which are complete intersections" by Haruhisa Nakajima and Kei-Ichi Watanabe, which is in the book Greco, Silvio, ...
1 vote
0 answers
136 views

Representations of finite groups over commutative rings-question and reference request

In a textbook of representation theory I have encountered the following statement without proof: Let $R$ be a commutative ring and $G$ a finite group. If $M$ is a simple $RG$-module then the ...
4 votes
0 answers
76 views

Minimal rank of a permutation resolution of a $G$-lattice

Let $G$ be a finite group. By a $G$-lattice I mean a finitely generated free abelian group $L$ with an action of $G$. One says that $L$ is a permutation lattice if $L$ has a $\mathbb{Z}$-basis ...
2 votes
0 answers
94 views

Why is the polynomial relating the invariants of a binary polyhedral group fixed by an overgroup?

Let $G$ be a finite subgroup of $\mathrm{SL}(2,\mathbb{C})$ and $N \triangleleft G$ a normal subgroup. Let $x, y, z$ be the fundamental invariants for the standard action of $N$ on $\mathbb{C}^2$, ...