Algebra Seminar

Yadira Valdivieso, Laval University

“Hochschild cohomology of Jacobian algebras from unpunctured surfaces: a geometric computation”

Let k be an algebraically closed field. A potential W for a quiver Q is a possibly infinite linear combination of cyclic paths in the complete path algebra k〈〈Q〉〉. The Jacobian algebra P(Q,W) associated to a quiver with a potential (Q,W) is the quotient of the complete path algebra k〈〈Q〉〉 modulo an ideal called Jacobian ideal J(W).

For any (tagged) triangulation T of a Riemann surface with marked points (S,M), it is possible to construct a finite dimensional Jacobian algebra AT. There are several examples in which algebraic properties of Jacobian algebras from (unpunctured) Riemann surfaces can be computed from the geometry of the Riemann surface.

In this talk, we show that the Hochschild cohomology of AT can be computed using the geometric data of the triangulated surface (S, M, T).

The necessary background and motivation will be given.

MC 5417

**Please Note Day and Room**