Related papers: Pascal's triangle and word bases for blob algebra …

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…

An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…

Let $n$ be a nonnegative integer, we use ribbon $n-$graph diagrams and the Yamada polynomial skein relations to construct an algebra ${\mathcal Y}_n$ which is shown to be closely related to the Temerley-Lieb Algebra. We prove that the…

The fundamental ideas of the definition of solvable and semisimple Bol algebras are given and some related theorems

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.

Let $(W,S)$ be an affine Coxeter system of type $\widetilde{B}$ or $\widetilde{D}$ and ${\rm TL}(W)$ the corresponding generalized Temperley-Lieb algebra. In this paper we define an infinite dimensional associative algebra made of decorated…

We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.

For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.

We study some non-semisimple representations of affine Temperley--Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite…

We give the description of three-dimensional Lie triple systems and their corresponding Lie algebras with invomorphisme, The description of three-dimensional Bol algebras linked with the distinguished Lie triple systems above is given. The…

The main result here gives an algebra(/linear category) isomorphism between a geometrically defined subcategory $J^1_0$ of a short Brauer category $J_0$ and a certain one-parameter specialisation of the blob category $b$. That is, we prove…

We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…

We show how the treatment of cellularity in families of algebras arising from diagram calculi, such as Jones' Temperley--Lieb wreaths, variants on Brauer's centralizer algebras, and the contour algebras of Cox et al (of which many algebras…

In the conference paper we construct analouge to Pascal's triangle that characterize primes with additional fascinating properties.

We describe and classify countable Boolean rings (which may or may not have a multiplicative identity) with finitely many distinguished ideals whose elementary theory is countably categorical. This extends the description by Macintyre and…

Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…

This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for…

This article deals with OLAP systems based on multidimensional model. The conceptual model we provide, represents data through a constellation (multi-facts) composed of several multi-hierarchy dimensions. In this model, data are displayed…

For a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the…

To any toric ideal $I_A$, encoded by an integer matrix $A$, we associate a matroid structure called {\em the bouquet graph} of $A$ and introduce another toric ideal called {\em the bouquet ideal} of $A$. We show how these objects capture…