Related papers: Universal Clone Algebra

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…

A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized…

Left and right "generalized Schur algebras", previously introduced by the author, are defined and analyzed. Filtrations of these algebras lead, in most cases, to parameterizations of the their irreducible representations over fields of…

In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…

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.

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using…

We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…

Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such…

We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.

Let $\Theta$ be a variety of algebras. In every $\Theta$ and every algebra $H$ from $\Theta$ one can consider algebraic geometry in $\Theta$ over $H$. We consider also a special categorical invariant $K_\Theta (H)$ of this geometry. The…

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".

We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie…

This article is devoted to the investigation of $B^*$-algebras, dual and annihilator ultranormed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and using them core radicals and radicals…

The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras…