44 citations · 110 across the 20 of their papers we have counts for
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Feigin and Odesskii's elliptic algebras
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
We study the elliptic algebras introduced by Feigin and Odesskii as a generalization of Sklyanin algebras. They form a family of quadratic algebras parametrized by c…
Non-exactness of direct products of quasi-coherent sheaves
Ryo Kanda
For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasi-coherent sheaves are not exact unless the scheme is a…
Extension groups between atoms in abelian categories
Ryo Kanda
We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelope…
Construction of Grothendieck categories with enough compressible objects using colored quivers
Ryo Kanda
We introduce a new method to construct a Grothendieck category from a given colored quiver. This is a variant of the construction used to prove that every partially ordered set ari…