11
votes
Accepted
Do acyclic amenable groups exist?
(1) Acyclic amenable groups do exist, because binate amenable groups exists: for instance, Philipp Hall's "universal locally finite group", which is by definition the Fraïssé limit of all ...
6
votes
Known posets of tilting modules for finite dimensional algebras
This is not really an answer but I don't have enough reputation to comment.
In the hereditary case, tilting modules and $\tau$-tilting modules coincide. Moreover the poset of tilting modules can be ...
5
votes
Accepted
Are projective tensor products left-exact if one considers only maps of norm at most 1?
The answer is no: the projective tensor product is not left-exact on $\mathrm{Ban}_1$.
There are several confusions in the question, that the following three points should hopefully clarify:
For ...
5
votes
Concrete examples of derived categories
One way to concretely describe derived categories is via the framework of model categories, and from the comments, it sounds like the OP is satisfied with this approach. Let $R$ be a commutative ring ...
3
votes
Accepted
Regular sequence in cohomology of Grassmannians
Modulo any prime ideal of the quotient ring, the product of polynomials
$$(1 + x_1 t + x_2 t^2 + \dots + x_m t^m) (1 + y_1 t + y_2 t^2 + \dots + y_n t^n ) $$ $$= 1 + (x_1+y_1) t + (x_2 + x_1 y_1 + y_2)...
2
votes
Infinite radical ideal cubed equals zero for tame hereditary Artin algebras
Any nonzero map between indecomposable preprojective modules cannot lie in the infinite radical.
For, we may as well assume the source is indecomposable projective. If there are $n$ indecomposable ...
1
vote
Accepted
Simplicial enrichment on unbounded algebras over an operad
There is no obstruction. If $M$ is a simplicial monoidal model category, and $O$ is an operad in $M$, then the category of $O$-algebras is simplicially enriched, tensored, and cotensored. If it's a ...
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