
The web algebra
Abstract In this paper we use Kuperberg's webs and Khovanov's foams to define a new algebra , which we call the web algebra. It is the analogue of Khovanov's arc algebra . We prove that is a graded symmetric Frobenius algebra. Furthermore, we categorify an instance of quantum skew Howe duality, which allows us to prove that is Morita equivalent to a certain, cyclotomic KLRalgebra. This allows us to determine the Grothendieck group of , to show that its center is isomorphic to the cohomology ring of a certain Spaltenstein variety, and to prove that is a graded cellular algebra.A few extra words The main idea of the web algebra is simple, i.e. given four webs and , which are the same at the boundary, one can define two new webs and by rotating and around the xaxis, switching their orientation and glue them on top of and . Then a multiplication of foams with the corresponding webs as boundary can be defined as follows:

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