Related papers: The Y-Product
We construct a faithful categorical action of the type $B$ braid group on the bounded homotopy category of finitely generated projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical…
We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…
We give a universal construction of families of Hopf $P$-algebras for any Hopf operad $P$. As a special case, we recover the Connes-Kreimer Hopf algebra of rooted trees.
In this review article we discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs we…
Given a finitely generated and projective Lie-Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and…
We announce the following result and give several applications: A Hamiltonian $T$-space (for $T$ a torus) with isolated fixed points is cobordant to a disjoint union of weighted projective spaces which are constructed from its fixed point…
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…
The notion of a Z-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethories can also be considered non-linear generalizations of…
We study the Hilbert series for $5d$ Superconformal Field Theories (SCFTs) engineered by Generalized Toric Polygons (GTPs), which extend the geometric realization of these theories from toric Calabi-Yau 3-folds to theories associated to…
We survey the theory of Hopf monads on monoidal categories, and present new examples and applications. As applications, we utilise this machinery to present a new theory of cross products, as well as analogues of the Fundamental Theorem of…
We endow twisted tensor products with a natural notion of counit and comultiplication, and we provide sufficient and necessary conditions making the twisted tensor product a counital coassociative coalgebra. We then characterize when the…
We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…
We define Calabi-Yau and periodic Frobenius algebras over arbitrary base commutative rings. We define a Hochschild analogue of Tate cohomology, and show that the "stable Hochschild cohomology" of periodic CY Frobenius algebras has a…
We discuss algebraic and representation theoretic structures in braided tensor categories C which obey certain finiteness conditions. Much interesting structure of such a category is encoded in a Hopf algebra H in C. In particular, the Hopf…
We develop a spectral sequence for the homotopy groups of Loday constructions with respect to twisted products in the case where the group involved is a constant simplicial group. We show that for commutative Hopf algebra spectra Loday…
In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace…
We prove a formula for the push-forward class of Bott-Samelson resolutions in the algebraic cobordism ring of the flag bundle. We specialise our formula to connective K-theory providing a geometric interpretation to the double…
The category of rational mixed Hodge-Tate structures is a mixed Tate category. So thanks to the Tannakian formalism, it is equivalent to the category of finite dimensional graded comodules over a graded commutative Hopf algebra H over Q.…