Related papers: On a presentation of the spin planar algebra

Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…

The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is…

We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.

This is a survey article for the forthcoming `A Concise Encyclopedia of Knot Theory.' We focus on the topology of spatial graphs with few vertices and edges, paying particular attention to Brunnian $\theta$-graphs.

The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…

This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and…

This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an…

Any variety of classical algebras has a so-called conformal counterpart. For example one can consider Lie conformal or associative conformal algebras. Lie conformal algebras are closely related to vertex algebras. We define free objects in…

When utilizing a cluster decomposible relativistic scattering formalism, it is most convenient that the covariant field equations take on a linear form with respect to the energy and momentum dispersion on the fields in the manner given by…

A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…

We introduce a graphical calculus for computing morphism spaces between the categorified spin networks of Cooper and Krushkal. The calculus, phrased in terms of planar compositions of categorified Jones-Wenzl projectors and their duals, is…

We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.

Let A be a finitely generated commutative algebra over a field K with a presentation A=K < X_{1}, ..., X_{n} | R >, where R is a set of monomial relations in the generators X_{1}, ..., X_{n}. So A = K[S], the semigroup algebra of the monoid…

Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of…

The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…

Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the literature. Partial classification of Hom-algebras over a PROP…

We describe the subfactor planar algebra of an intermediate subfactor $N\subset Q \subset M$ of an extremal subfactor $N\subset M$ of finite Jones index which is not necessarily irreducible.