7
$\begingroup$

Let $W$ be a Coxeter group. The Iwahori-Hecke algebra $H_q(W)$ is a deformation of $k W$.

Question: is there some way to interpret the deformation $H_q(W)$ as a cohomology class? It doesn't seem like $kW$ twisted by a class in $H^2(W,k^{\times})$...

$\endgroup$
10
$\begingroup$

Not in an interesting way. Cohomology classes describe formal deformations (i.e. deformations over an Artinian ring, or more generally complete local rings), and the Iwahori-Hecke algebra is trivial on a formal neighborhood of $q=1$. In fact, the only points where it is not trivial on a formal neighborhood is when $q$ is a root of unity of small order.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.