Trace as an alternative decategorification functor

Abstract

Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" functor. Algebras are typically categorified to additive categories with additional structure and decategorification is usually given by the (split) Grothendieck group. In this expository article we study an alternative decategorification functor given by the trace or the zeroth Hochschild--Mitchell homology. We show that this form of decategorification endows any 2-representation of the categorified quantum sl(n) with an action of the current algebra U(sl(n)[t]) on its center.

47 pages with tikz figures. arXiv admin note: text overlap with arXiv:1405.5920 by other authors

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Cited by in corpus (10)

• On the center of quiver-Hecke algebras
• 3d-3d correspondence for mapping tori
• Trace decategorification of the Hecke category
• Current algebras and categorified quantum groups
• The Elliptic Hall algebra and the deformed Khovanov Heisenberg category
• A graphical calculus for the Jack inner product on symmetric functions
• W-algebras from Heisenberg categories
• Affinization of monoidal categories
• Trace of the twisted Heisenberg Category
• Frobenius W-algebras and traces of Frobenius Heisenberg categories