Related papers: Soft Neutrosophic Algebraic Structures and Their G…
We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott-Tomforde-Willis subshifts in terms of a…
After a short review of the algebraic setting of N=2 superconformal field theories, their chiral ring and their perturbations, I present some recent results on curious relations between the integrability of their perturbations and algebraic…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…
This paper, together with a forthcoming paper by the author and Seitz, proves the Margulis-Platonov conjecture concerning the normal subgroup structure of algebraic groups over number fields, in the case of inner forms of anisotropic groups…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
Generalizing supertropical algebras, we present a "layered" structure, "sorted" by a semiring which permits varying ghost layers, and indicate how it is more amenable than the "standard" supertropical construction in factorizations of…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
In this paper, we introduce semiopen and semiclosed fuzzy soft sets in fuzzy soft topological spaces. Various properties of these sets are studied alongwith some characterizations. Further, we generalize the structures like interior and…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras. The elements of these rings are residue classes of unions of certain labeled graphs that were used to construct canonical bases in…
By omitting the unitary constraint from the definition of weak post-Hopf algebras, we introduce the concept of relaxed weak post-Hopf algebras, offering a thorough characterization of all feasible relaxed weak post-Hopf algebraic structures…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…
We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a…
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…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
In this paper we show how the hyperstructure concept leads to new algebraic structures and general field theories.