# Seminars & Colloquia Calendar

## Cohomological criterion of reductivity for associative algebras

#### Fei Qi, Rutgers University

Location: ** Hill GSL**

Date & time: Friday, 29 September 2017 at 2:30PM - 3:30PM

Abstract: |
I will give the definitions to the Hochschild cohomology to associative algebras and prove the reducitivity theorem: an associative algebra A is semisimple if and only if the Hochschild cohomology HH^1(A, M) = 0 for every bimodule M. The proof of the if part is elementary and can be easily understood (though somehow tricky). The proof of the only if part will have to use the Artin-Wedderburn theory. If time allows, I will also talk about the generalizations of these proofs to vertex algebra (joint with Huang). |
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