Related papers: On factorization algebras arising in the quantum g…
Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…
Given a finite crystallographic root system $\Phi$ whose Dynkin diagram has a non-trivial automorphism, it yields a new root system $\Phi_{\tau}$ by a so-called classical folding. On the other hand, Lusztig's folding (1983) folds the root…
In this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To…
As observed by Kawamata, a $\mathbb{Q}$-Gorenstein smoothing of a Wahl singularity gives rise to a one-parameter flat degeneration of a matrix algebra. A similar result holds for a general smoothing of any two-dimensional cyclic quotient…
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We study the Hopf algebra structure of Lusztig's quantum groups. First we show that the zero part is the tensor product of the group algebra of a finite abelian group with the enveloping algebra of an abelian Lie algebra. Second we build…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
We derive a class of cubic interaction vertices for three higher spin fields, with integer spins $\lambda_1$, $\lambda_2$, $\lambda_3$, by closing commutators of the Poincar\'e algebra in four-dimensional flat spacetime. We find that these…
We prove that the Kauffman bracket skein algebra of a cylinder over a surface with boundary, defined over complex numbers, is isomorphic to the observables of an appropriate lattice gauge field theory.
Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real…
Let $C$ be a curve in $\mathbb{P}^4$ and $X$ be a hypersurface containing it. We show how it is possible to construct a matrix factorization on $X$ from the pair $(C,X)$ and, conversely, how a matrix factorization on $X$ leads to curves…
We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
If $G$ is a strongly connected finite directed graph, the set $\mathcal{T}G$ of rooted directed spanning trees of $G$ is naturally equipped with a structure of directed graph: there is a directed edge from any spanning tree to any other…
We compute the K-theory of a collection of C*-algebras, which we refer to as boundary C*-algebras, arising as the crossed product C*-algebras of lattice actions on the maximal Furstenberg boundaries of symmetric spaces of noncompact type.…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We discuss factorization of the Dyson--Schwinger equations using the Lie- and Hopf algebra of graphs. The structure of those equations allows to introduce a commutative associative product on 1PI graphs. In scalar field theories, this…
We construct a factorization algebra, via the factorization envelope, starting from a Lie conformal algebra, and prove that the associated vertex algebra is isomorphic to its enveloping vertex algebra. Our construction generalizes the…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\Delta_z) starting from the Lie bialgebra (g,\delta) that gives the first-order deformation of the coproduct map \Delta_z is presented.…