Results 41 to 50 of about 5,500 (151)

An infinite torus braid yields a categorified Jones-Wenzl projector [PDF]

, 2010
A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a ...
Rozansky, Lev
core  

A Hilton–Milner theorem for exterior algebras

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract Recent work of Scott and Wilmer and of Woodroofe extends the Erdős–Ko–Rado theorem from set systems to subspaces of k$k$‐forms in an exterior algebra. We prove an extension of the Hilton–Milner theorem to the exterior algebra setting, answering in a strong way a question asked by these authors.
Denys Bulavka, Francesca Gandini, Russ Woodroofe   +2 more
wiley   +1 more source

Categorification of the Jones–Wenzl projectors

Quantum Topology, 2012
The Jones–Wenzl projectors p_n play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes P_n , whose graded Euler ...
Cooper, Benjamin, Krushkal, Vyacheslav
openaire   +4 more sources

Trace as an alternative decategorification functor [PDF]

, 2014
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.
A Al-Nofayee, A Cȧldȧraru, A Joyal, AD Lauda, AD Lauda, AD Lauda, B Cooper, B Mitchell, C Blanchet, D Bar-Natan, D Bar-Natan, D Kazhdan, F Borceux, G Kuperberg, G Lusztig, G Lusztig, G Lusztig, H Garland, IG Macdonald, J Baez, J Brundan, J Brundan, J Brundan, J Brundan, J Milnor, J Rosenberg, JL Loday, JRB Cockett, LH Kauffman, M Kashiwara, M Kashiwara, M Khovanov, M Khovanov, M Khovanov, M Khovanov, M Mackaay, M Müger, M Varagnolo, N Ganter, N Geer, N Reshetikhin, R Penrose, V Ginzburg, VG Turaev   +43 more
core   +1 more source

Floer theory for the variation operator of an isolated singularity

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analog for an isolated singularity. We define the monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the ...
Hanwool Bae, Cheol‐Hyun Cho, Dongwook Choa, Wonbo Jeong   +3 more
wiley   +1 more source

Categorification of the elliptic Hall algebra

Documenta Mathematica, 2022
We show that the central charge k reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge
Mousaaid, Youssef, Savage, Alistair
openaire   +3 more sources

Heisenberg and Kac–Moody categorification [PDF]

Selecta Mathematica, 2020
We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac-Moody 2-category (and vice versa). This gives a way to construct Kac-Moody actions in many representation-theoretic examples which is independent of Rouquier'
Jonathan Brundan, Alistair Savage, Ben Webster   +2 more
openaire   +3 more sources

Remarks on some infinitesimal symmetries of Khovanov–Rozansky homologies in finite characteristic

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3597-3613, November 2025.
Abstract We give a new proof of a theorem due to Shumakovitch and Wang on base point independence of Khovanov–Rozansky homology in characteristic p$p$. Some further symmetries of gl(p)$\mathfrak {gl}(p)$‐homology in characteristic p$p$ are also discussed.
You Qi, Louis‐Hadrien Robert, Joshua Sussan, Emmanuel Wagner   +3 more
wiley   +1 more source

Linearization and categorification [PDF]

Portugaliae Mathematica, 2016
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum link invariants. We also review categorification, which adds an additional layer of structure, in the context of the last two examples.
openaire   +2 more sources

Global bases for Bosonic extensions of quantum unipotent coordinate rings

Proceedings of the London Mathematical Society, Volume 131, Issue 2, August 2025.
Abstract In the paper, we establish the global basis theory for the bosonic extension Â$\widehat{\mathcal {A}}$ associated with an arbitrary symmetrizable generalized Cartan matrix. When Â$\widehat{\mathcal {A}}$ is of simply laced finite type, Â$\widehat{\mathcal {A}}$ is isomorphic to the quantum Grothendieck ring Kq(Cg0)$\mathcal {K}_q(\mathcal ...
Masaki Kashiwara, Myungho Kim, Se‐jin Oh, Euiyong Park   +3 more
wiley   +1 more source