Related papers: Quadratic Tangles in Planar Algebras
For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…
We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most…
We find the connection between 3-dimensional commutative algebras with a trivial trace and plane quartics and its bitangents.
We construct a polynomial planar vector field of degree two with one invariant algebraic curves of large degree. We exhibit an explicit quadratic vector fields which invariant curves of degree nine, twelve, fifteen and eighteen degree.
We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…
We give graphical presentations for the two quantum subgroups of type $G_2$. To do this we use a method of extending a tensor category by embedding the planar algebra of a $\otimes$-generating object into the graph planar algebra of this…
We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxter relation planar algebras. We present the skein theoretic…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
We describe an explicit finite presentation for a finite depth subfactor planar algebra. We also show that such planar algebras are singly generated with the generator subject to finitely many relations.
We give generators and relations for the planar algebras corresponding to $ADE$ subfactors. We also give a basis and an algorithm to express an arbitrary diagram as a linear combination of these basis diagrams.
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
Parallel lines are very important objects in Euclid plane geometry and its behaviors can be gotten by one's intuition. But in a planar map geometry, a kind of the Smarandache geometries, the sutation is complex since it may contains…
The similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
We show that it is possible to decide whether a given planar diagram correctly depicts the spatial figure consisting of a planar quadrangle together with its shadow in another plane.
In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.