Speaker: Dr.Fei Qi（Yale University）

Title: Cohomology theory of meromorphic open-string vertex algebras

Time: Thur, Jun.6, 2019, PM:16:00-17:00

Location: Room 4131, Building No.4, Wushan Campus

Abstract:

      In the study of associative algebras and modules, cohomology theory plays an important role. In particular, the first Hochschild cohomology is a vector space isomorphic to the space of outer derivations; if the first cohomology vanishes for every bimodule, then every left module for the algebra is completely reducible; and the second Hochschild cohomology is in one-to-one correspondence with the set of first-order deformations of the algebra. We would like to develop cohomology methods for vertex algebras. A vertex algebra is the algebraic structure formed by vertex operators, which are suitable infinite series of endomorphisms on a vector space. These vertex operators satisfy conditions that are analogous to those in a commutative associative algebra. YiZhi Huang discovered in 2012 that the cohomology theory can also be defined for grading-restricted vertex algebras and obtained analogues of some of the previously mentioned results. Joint with Huang, the speaker generalized the theory for meromorphic open-string vertex algebras (where commutativity does not hold and can be viewed as analogues of noncommutative associative algebras) that are not necessarily grading-restricted and obtained analogues of all the previously mentioned results.