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Betti numbers of split graphs

math.AC · 2026-06-02 · unverdicted · novelty 6.0

Betti numbers of edge rings of split graphs are fully determined and depend only on the multiset of neighbor counts from the complete part to the stable part.

Rigidity and Cohomology of Seaweed Lie Algebras

math.RA · 2026-04-20 · unverdicted · novelty 6.0

Indecomposable seaweed subalgebras of complex simple Lie algebras have vanishing adjoint cohomology and are absolutely rigid; decomposable ones have cohomology determined solely by their center via the Coll-Gerstenhaber decomposition.

On the category of semi-graded modules

math.CT · 2026-05-25 · unverdicted · novelty 5.0

SGR-R possesses a canonical set of free generators via shifted twists, endowing it with a Grothendieck structure and enough injectives and projectives, plus a semi-graded Baer's criterion analogue.

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  • On the category of semi-graded modules math.CT · 2026-05-25 · unverdicted · none · ref 24

    SGR-R possesses a canonical set of free generators via shifted twists, endowing it with a Grothendieck structure and enough injectives and projectives, plus a semi-graded Baer's criterion analogue.