Related papers: An AF algebra associated with the Farey tessellati…
We give an elementary proof of a theorem that characterizes quasisymmetric maps of the unit circle in terms of shear coordinates on the Farey tesselation. The proof only uses the normal family argument for quasisymmetric maps and some…
We construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke algebras. The center of the affine Hecke…
Vertex algebras are equivalent to translation-equivariant chiral algebras on $\mathbb{A}^1$, in the sense of Beilinson and Drinfeld. In this paper we give an algebraic construction of a chiral algebra on $\mathbb{A}^n$; this can be seen as…
Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relationship, in the form of a diagrammatic calculus of string…
We study topological aspects of the category of abstract Cuntz semigroups, termed Cu. We provide a suitable setting in which we are able to uniformly control how to approach an element of a Cu-semigroup by a rapidly increasing sequence.…
We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an "affine" version of the construction of [14]. Explicitly, we show that the aforementioned trace is generated by the objects…
In this note, we introduce a class of algebras that are in some sense related to conformal algebras. This class (called TC-algebras) includes Weyl algebras and some of their (associative and Lie) subalgebras. By a conformal algebra we…
Algebraic-geometrical n-orthogonal curvilinear coordinate systems in a flat space are constructed. They are expressed in terms of the Riemann theta function of auxiliary algebraic curves. The exact formulae for the potentials of algebraic…
We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…
We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y=0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum…
In this note we associate to each Frobenius algebra a vertex algebra, the simplest example being the Virasoro vertex algebra. This construction is analogous to the procedure which associates to a Lie algebra with an invariant bilinear form…
We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew…
The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.
The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras. Our research focuses on studying characters and Cartan automorphisms, which appear in the…
We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose…
In the continuity of our previous paper arXiv:1509.05516, we define three new algebras, $A_{n}(a,b,c)$, $B_{n}$ and $C_{n}$, that are close to the braid algebra. They allow to build solutions to the braided Yang-Baxter equation with…
An algebra is said to be hopfian if it is not isomorphic to a proper quotient of itself. We describe several classes of hopfian and of non-hopfian unital lattice-ordered abelian groups and MV-algebras. Using Elliott classification and…
We give a procedure to compute the rational homotopy groups of the group of quasi-unitaries of an AF-algebra. As an application, we show that an AF-algebra is K-stable if and only if it is rationally K-stable.
Gendo-Frobenius algebras are a common generalisation of Frobenius algebras and of gendo-symmetric algebras. A comultiplication is constructed for gendo-Frobenius algebras, which specialises to the known comultiplications on Frobenius and on…
We investigate associative quotients of vertex algebras. We also give a short construction of the Zhu algebra, and a proof of its associativity using elliptic functions.