Results 1 to 10 of about 5,431 (90)
A Diagrammatic Temperley-Lieb Categorification [PDF]
International Journal of Mathematics and Mathematical Sciences, 2010 The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane.
Ben Elias
doaj +4 more sources
Landauer’s Principle as a Special Case of Galois Connection [PDF]
Entropy, 2018 It is demonstrated how to construct a Galois connection between two related systems with entropy. The construction, called the Landauer’s connection, describes coupling between two systems with entropy.
Radosław A. Kycia
doaj +2 more sources
A Categorification of One-Variable Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We develop a diagrammatic categorification of the polynomial ring $\mathbb{Z} [x]$, based on a geometrically-defined graded algebra and show how to lift various operations on polynomials to the categorified setting.
Mikhail Khovanov, Radmila Sazdanovic
doaj +1 more source
Mathematics, 2022 Let CAn=C[S2≀S2≀⋯≀S2] be the group algebra of an n-step iterated wreath product. We prove some structural properties of An such as their centers, centralizers, and right and double cosets.
Mee Seong Im, Can Ozan Oğuz
doaj +1 more source
Partial categorification of Hopf algebras and representation theory of towers of \mathcalJ-trivial monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper considers the representation theory of towers of algebras of $\mathcal{J} -trivial$ monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings $G_0 ...
Aladin Virmaux
doaj +1 more source
Mathematics, 2022 The four subspace problem is a known matrix problem, which is equivalent to determining all the indecomposable representations of a poset consisting of four incomparable points.
Agustín Moreno Cañadas +2 more
doaj +1 more source
Homotopies of 2-Algebra Morphisms
Communications in Advanced Mathematical Sciences, 2022 In [1] it is defined the notion of 2-algebra as a categorification of algebras, and shown that the category of strict 2-algebras is equivalent to the category of crossed modules in commutative algebras.
Ummahan Ege Arslan, İbrahim Akça
doaj +1 more source
Journal of High Energy Physics, 2022 We concentrate on a treatment of a Higgs-Coulomb duality as an absence of manifest phase transition between ordered and disordered phases of 2d N $$ \mathcal{N} $$ = (2, 2) theories.
Dmitry Galakhov
doaj +1 more source
Axioms, 2012 We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid—the category of permutation representations of a finite group.
Alexander E. Hoffnung
doaj +1 more source
Fivebranes and 3-manifold homology
Journal of High Energy Physics, 2017 Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds.
Sergei Gukov, Pavel Putrov, Cumrun Vafa
doaj +1 more source