Timeline for Hochschild homology of upper triangular matrix algebra?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2014 at 19:11 | vote | accept | Leo | ||
| Mar 9, 2014 at 11:32 | comment | added | Dag Oskar Madsen | Yes, that is an important assumption, we have for instance $HH_1(K[X]) \neq 0$ although $gldim(K[X])=1 < \infty$. | |
| Mar 9, 2014 at 9:48 | comment | added | Mariano Suárez-Álvarez | One significant assumption for the result Dag mentions is that the algebra be finite dimensional, iirc. | |
| Mar 8, 2014 at 1:48 | comment | added | Mariano Suárez-Álvarez | @LeonLampret, every (admissible) quotient of a path algebra has a very well understood basis (and, interpreting this correctly, every álgebra is of this form) I suggest you look at the literature for papers which do computations. | |
| Mar 8, 2014 at 0:56 | comment | added | Dag Oskar Madsen | @LeonLampret One important result is that if the algebra $A$ is of finite global dimension, then (with some mild assumptions) $HH_{\ast}(A)$ is concentrated in degree $0$ by Proposition 2.5 in [Keller, Bernhard. Invariance and localization for cyclic homology of DG algebras. J. Pure Appl. Algebra 123 (1998), no. 1-3, 223--273.] | |
| Mar 8, 2014 at 0:27 | comment | added | Leo | Any concrete examples of families of (commutative or noncommutative) finite-dimensional $K$-algebras which have a clear $K$-module basis but $HH_\ast$ has not yet been computed? I need good examples to try and test Algebraic Morse Theory (eventually for an article), but I'm not familiar with the state-of-the-art. BTW, what is the best literature for $HH$, besides Weibel or Loday? | |
| Mar 7, 2014 at 20:07 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 3.0 |
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| Mar 7, 2014 at 19:47 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 3.0 |
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| Mar 7, 2014 at 19:42 | comment | added | Mariano Suárez-Álvarez | Morally, the complex which computes $HH_*(A)$, starting from the resolution above, only sees cycles in the quiver, so if there are none of them, it is very easy to handle. Now, if there are cycles, there be dragons! :-) | |
| Mar 7, 2014 at 19:40 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 3.0 |