Related papers: Ore's theorem on subfactor planar algebras

We show that every 2nd order ODE defines a 4-parameter family of projective connections on its 2-dimensional solution space. In a special case of ODEs, for which a certain point transformation invariant vanishes, we find that this family of…

One of the earliest results in enumerative combinatorial geometry is the following theorem of de Bruijn and Erd\H{o}s: Every set of points $E$ in a projective plane determines at least $|E|$ lines, unless all the points are contained in a…

We show Lie algebra versions of some results on homological finiteness properties of subdirect products of groups, including a version of the 1-2-3 Theorem.

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Jones conjectures the arboreal representation of a degree two rational map will have finite index in the full automorphism group of a binary rooted tree except under certain conditions. We prove a version of Jones' Conjecture for quadratic…

We establish new restrictions on the values of the lifting obstruction for projective unitary representations of second countable, locally compact Hausdorff groups on operator algebras. Using these, we show that every projective…

It is a fairly known fact that most of the algebras appearing in the theory of rings of differential operators, quantized algebras of different kinds (including many quantum groups), regular algebras in projective non-commutative geometry,…

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.

The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…

Let $\mathcal{M}$ be a type ${\rm II_1}$ factor and let $\tau$ be the faithful normal tracial state on $\mathcal{M}$. In this paper, we prove that given an $X \in \mathcal{M}$, $X=X^*$, then there is a decomposition of the identity into $N…

William Thurston (1946-2012) gave a combinatorial characterization for generic branched self-coverings of the two-sphere by associating a planar graph to them 10.48550/arXiv.1502.04760. By generalizing the notion of local balancing, the…

Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every…

For simple Lie algebras we construct characteristic identities for split (polarized) Casimir operators in representations $T \otimes Y_n$ and $T \otimes Y_n'$, where $T$ -- defining (minimal fundamental for exceptional Lie algebras)…

We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…

In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…

To a weighted graph can be associated a bipartite graph planar algebra P. We construct and study the symmetric enveloping inclusion of P. We show that this construction is equivariant with respect to the automorphism group of P. The…

This is an old paper put here for archeological purposes. It is proved that a finite-dimensional Lie algebra over a field of characteristic p>5, that can be written as a vector space (not necessarily direct) sum of two nilpotent…

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real…

We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system…