“On the formal Peterson subalgebra and its dual”
Venerdì 18 Ottobre 2024, ore 12:30 - Aula 2BC30 - Kirill Zaynullin (University of Ottawa)
Abstract
We discuss a generalization of the Peterson subalgebra to a generalized (oriented) cohomology theory which we call the formal Peterson subalgebra.
One of our results shows that the localized formal Peterson subalgebra for the extended Dynkin diagram of type $\hat A_1$ provides an algebraic model for “quantum generalized cohomology” of the projective line. Hence, confirming and extending the Peterson conjecture for these settings.
We also prove that the dual of the formal Peterson subalgebra (a generalized cohomology of the affine Grassmannian) is the $0$th Hochschild homology of the formal affine Demazure algebra. Hence, extending the techniques and results on the Hopf algebroids of structure algebras of moment graphs by [Lanini-Xiong-Z.] to the case of affine root systems.
