Related papers: On a presentation of the spin planar algebra
We consider supersymmetry algebras in space-times with arbitrary signature and minimal number of spinor generators. The interrelation between super Poincar\'e and super conformal algebras is elucidated. Minimal super conformal algebras are…
We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of…
There is a natural construction which associates to a finitely generated, countable, discrete group $G$ and a 3-cocycle $\omega$ of $G$ an inclusion of II$_1$ factors, the so-called diagonal subfactors (with cocycle). In the case when the…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
In this paper, we construct the "2221" subfactor planar algebra by finding it as a subalgebra of the graph planar algebra of its principal graph. In particular, we give a presentation of the "2221" subfactor planar algebra consisting of…
Factoring out the spin $1$ subalgebra of a $ W $ algebra leads to a new $ W $ structure which can be seen either as a rational finitely generated $ W $ algebra or as a polynomial non-linear $ W_\infty$ realization.
By changing to an orthogonal basis, we give a short proof that the subfactor of the graded algebra of a planar algebra reproduces the planar algebra.
We give a diagrammatic presentation of the A_2-Temperley-Lieb algebra. Generalizing Jones' notion of a planar algebra, we formulate an A_2-planar algebra motivated by Kuperberg's A_2-spider. This A_2-planar algebra contains a subfamily of…
Let $A$ be an associative algebra with identity and with trace. We study the family of planar algebras on 1-boxes that arise from $A$ in the work of Jones, but with the added assumption that the labels on the 1-boxes come from a discrete…
To a planar algebra P in the sense of Jones we associate a natural non- commutative ring, which can be viewed as the ring of non-commutative polynomials in several indeterminates, invariant under a symmetry encoded by P. We show that this…
Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.
We consider a construction of the fundamental spin representations of the simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a…
We define a family of structures called "opetopic algebras", which are algebraic structures with an underlying opetopic set. Examples of such are categories, planar operads, and Loday's combinads over planar trees. Opetopic algebras can be…
Let $K\langle X\rangle =K\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over a field $K$, and let $R\langle X\rangle =R\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over an arbitrary commutative ring…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.
We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl…
A general simplicity problem in category theory is proposed. A particular example, the simplest choice of generators of an algebra is specified and illustrated by an example.
For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.
The relations between integrable Poisson algebras with three generators and two-dimensional manifolds are investigated. Poisson algebraic maps are also discussed.