Algebra seminar: Superalgebra deformations of the web categories

Abstract: Planar graphs such as Temperley-Lieb diagrams and spiders first appear as a diagrammatic tool to study tensor invariants for the Lie algebras sl_2 and sl_3 over a field. Cautis-Kamnitzer-Morrison then generalized this to higher ranks, where webs describe all morphisms in a subcategory of gl_n modules generated by exterior powers of the natural module. Tubbenhauer-Vaz-Wedrich gave a further generalization to mixed tensor products involving symmetric powers. In this joint work with N. Davidson, R. Muth and J. Kujawa, we study symmetric webs for gl_n(A), where A is a locally unital superalgebra. We described morphisms using a functor from the A-web category to the corresponding module category for gl_n(A). We also give a web formulation of the Schur algebra and explore the condition on A such that such a functor is full (for example, when A is finite-dimensional semisimple). Several interesting examples include the cases when A is the Clifford algebra and the zigzag algebra.

Participate on site or via Zoom (meeting ID: 645 5572 6999, for passcode: please contact the organizer).