Related papers: Equations over direct powers of algebraic structur…
In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.
All exactly integrable systems connected with the semisimple algebras of the second rank with an arbitrary choice of the grading in them are presented in explicit form. General solution of such systems are expressed in terms of the matrix…
We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2…
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying…
Given a relation on $ X \times Y $, we can construct two abstract simplicial complexes called Dowker complexes. The geometric realizations of these simplicial complexes are homotopically equivalent. We show that if two relations are…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
In this paper, we give matrix formulae for non-orientable surfaces that provide the Laurent expansion for quasi-cluster variables, generalizing the orientable surface matrix formulae by Musiker-Williams. We additionally use our matrix…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
Quasi relation algebras (qRAs) were first described by Galatos and Jipsen in 2013. They are generalisations of relation algebras and can also be viewed as certain residuated lattice expansions. We identify positive symmetric idempotent…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
The aim of this paper is to give all quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of $\Bbbk\mathbb{Z}_{2}$ by $\Bbbk^G$ for an abelian group $G$. We first introduce the concept of…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…
In this paper we extend the almost complex Poisson structures from almost complex manifolds to almost complex Lie algebroids. Examples of such structures are also given and the almost complex Poisson morphisms of almost complex Lie…
We define a "quantum relation" on a von Neumann algebra M \subset B(H) to be a weak* closed operator bimodule over its commutant M'. Although this definition is framed in terms of a particular representation of M, it is effectively…
We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…