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 ...
Nicolas Monod's user avatar
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 ...
Baptiste Rognerud's user avatar
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 ...
Mikael de la Salle's user avatar
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 ...
David White's user avatar
  • 29.4k
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)...
Will Sawin's user avatar
  • 135k
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 ...
Andrew Hubery's user avatar
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 ...
David White's user avatar
  • 29.4k

Only top scored, non community-wiki answers of a minimum length are eligible