Related papers: Augmented down-up algebras and uniform posets
The method of double extension, introduced by A.~Medina and Ph.~Revoy, is a procedure which decomposes a Lie algebra with an invariant symmetric form into elementary pieces. Such decompositions were developed for other algebras, for…
We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner. We present several examples of quadri-algebras: the…
We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on algebraic curves. Our approach features three…
Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of…
We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…
We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
Centraliser algebras of monomial representations of finite groups may be constructed and studied using methods similar to those employed in the study of permutation groups. Guided by results of D. G. Higman and others, we give an explicit…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…
To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these…
We introduce the notion of P-polynomial coherent configurations and show that they can have at most two fibres. We then introduce a class of two-fibre coherent configurations which have two distinguished bases for the coherent algebra,…
A compatible associative algebra is a vector space endowed with two associative multiplication operations that satisfy a natural compatibility condition. In this paper, we investigate and classify compatible pairs of associative algebras of…
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical…
We consider a class of Poincar\'e superalgebras for which the nested bracket of three supercharges is necessarily zero only in dimensions greater than three. In lower dimensions, we give a precise characterisation of the data which encodes…
The way to arrive at formula of zeta matrix for any graded posets with the finite set of minimal elements is delivered following the first reference. This is being achieved via adjacency and zeta matrix description of bipartite digraphs…
In 1986 Stanley associated to a poset the order polytope. The close interplay between its combinatorial and geometric properties makes the order polytope an object of tremendous interest. Double posets were introduced in 2011 by Malvenuto…
We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation DU - qUD = rI. We construct examples based upon: the Fibonacci poset, permutations, standard Young tableau, and plane binary…