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A Note on the Grothendieck Group of an Additive Category

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arxiv 1109.2040 v1 pith:EUB335EN submitted 2011-09-09 math.CT math.QA

David E. V. Rose This is my paper · ORCID
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keywords categorygrothendieckgroupadditivegroupshomotopyabelianalong
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There are two abelian groups which can naturally be associated to an additive category A: the split Grothendieck group of A and the triangulated Grothendieck group of the homotopy category of (bounded) complexes in A. We prove that these groups are isomorphic. Along the way, we deduce that the `Euler characteristic' of a complex in A is invariant under homotopy equivalence.

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  1. Induction for extended affine type A Soergel bimodules: first steps

    math.RT 2025-07 accept novelty 6.0 of 10

    A categorical embedding Ψ for extended affine type A Soergel bimodules is constructed, categorifying the Hecke algebra parabolic embedding, with an example categorifying the Zelevinsky tensor product of two trivial re...

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