Related papers: Compatible associative products and trees
We expand the existing arsenal of methods for exploring the irreducible components of the varieties $Rep(A,\bold d)$ which parametrize the representations with dimension vector $\bold d$ of a finite dimensional algebra $A$. To do so, we…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
We consider crossed product von Neumann algebras arising from free Bogoljubov actions of the integers. We describe several presentations of them as amalgamated free products and cocycle crossed products and give a criterion for…
Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of $m\times n$ rank-2 matrices and $n\times n$ skew-symmetric…
We introduce the combinatorial notion of posetted trees and we use it in order to write an explicit expression of the Baker-Campbell-Hausdorff formula.
We investigate graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties) as polytopal analogues of vector spaces. In many cases we show that these retracts are again polytopal…
We study and classify faithfully balanced modules for the algebra of lower triangular $n$ by $n$ matrices. The theory extends known results about tilting modules, which are classified by binary trees, and counted with the Catalan numbers.…
The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated free group factor $L(\freeF_r)$. The finite…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where…
The extending structures and unified products for Zinbiel algebras are developed. Some special cases of unified products such as crossed products and matched pair of Zinbiel algebras are studied. It is proved that the extending structures…
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.
Using a family of graded algebra structures on a planar algebra and a family of traces coming from random matrix theory, we obtain a tower of non-commutative probability spaces, naturally associated to a given planar algebra. The associated…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…
Associative or Jordan algebras generated by two idempotents are described precisely.
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yields a new formula for the number of NATs. We also obtain…
We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
The homology of free Lie algebras with coefficients in tensor products of the adjoint representation working over Q contains important information on the homological properties of polynomial outer functors on free groups. The latter…