Results 61 to 70 of about 5,500 (151)
Semistable torsion classes and canonical decompositions in Grothendieck groups
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract We study two classes of torsion classes that generalize functorially finite torsion classes, that is, semistable torsion classes and morphism torsion classes. Semistable torsion classes are parametrized by the elements in the real Grothendieck group up to TF equivalence.
Sota Asai, Osamu Iyama
wiley +1 more source
Categorification of a frieze pattern determinant [PDF]
Journal of Combinatorial Theory, Series A, 2012 14 pages; 8 figures. Sections 1-3 rewritten, postponing the cluster interpretation until Section 3.
Karin Baur, Robert J. Marsh
openaire +2 more sources
Grothendieck groups and a categorification of additive invariants
, 2011 A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up
Aluffi P. +18 more
core +1 more source
Link splitting deformation of colored Khovanov–Rozansky homology
Proceedings of the London Mathematical Society, Volume 129, Issue 3, September 2024.Abstract We introduce a multiparameter deformation of the triply‐graded Khovanov–Rozansky homology of links colored by one‐column Young diagrams, generalizing the “y$y$‐ified” link homology of Gorsky–Hogancamp and work of Cautis–Lauda–Sussan. For each link component, the natural set of deformation parameters corresponds to interpolation coordinates on ...
Matthew Hogancamp +2 more
wiley +1 more source
Solution of a problem in monoidal categorification by additive categorification
Journal of AlgebraIn 2021, Kashiwara-Kim-Oh-Park constructed cluster algebra structures on the Grothendieck rings of certain monoidal subcategories of the category of finite-dimensional representations of a quantum loop algebra, generalizing Hernandez-Leclerc's pioneering work from 2010. They stated the problem of finding explicit quivers for the seeds they used.
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Advances in R-matrices and their applications (after Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,...)
, 2017 R-matrices are the solutions of the Yang-Baxter equation. At the origin of the quantum group theory, they may be interpreted as intertwining operators. Recent advances have been made independently in different directions.
Hernandez, David
core +1 more source
Support varieties without the tensor product property
Bulletin of the London Mathematical Society, Volume 56, Issue 6, Page 2150-2161, June 2024.Abstract We show that over a perfect field, every non‐semisimple finite tensor category with finitely generated cohomology embeds into a larger such category where the tensor product property does not hold for support varieties.
Petter Andreas Bergh +2 more
wiley +1 more source
Picard sheaves, local Brauer groups, and topological modular forms
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We develop tools to analyze and compare the Brauer groups of spectra such as periodic complex and real K$K$‐theory and topological modular forms, as well as the derived moduli stack of elliptic curves. In particular, we prove that the Brauer group of TMF$\mathrm{TMF}$ is isomorphic to the Brauer group of the derived moduli stack of elliptic ...
Benjamin Antieau +2 more
wiley +1 more source
A horizontal categorification of Gel'fand duality
Advances in Mathematics, 2011 22 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, one section added, to appear in Advances in ...
Bertozzini, Paolo +2 more
openaire +3 more sources