Related papers: Almost symmetric numerical semigroups
In this paper, we introduce and investigate a new notion of exact sequences of semimodules over semirings relative to the canonical image factorization. Several homological results are proved using the new notion of exactness including some…
Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\Gamma <G$ and $\Lambda < G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $\Gamma$ into…
A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…
Let F be the free group over a set of two or more generators. R. Brooks constructed an infinite family of quasi-morphisms on F such that an infinite subfamily gives rise to independent classes in the second bounded cohomology of F, which…
A numerical semigroup is an additive submonoid of the natural numbers with finite complement. The size of the complement is called the genus of the semigroup. How many numerical semigroups have genus equal to $g$? We outline Zhai's proof of…
We say that a subset $X$ quasi-isometrically boundedly generates a finitely generated group $\Gamma$ if each element $\gamma$ of a finite-index subgroup of $\Gamma$ can be written as a product $\gamma = x_1 x_2 \cdots x_r$ of a bounded…
This is a revised version of the previous version with a new appendix consisting of characteristic two case. We define quasi-quadratic modules in a commutative ring generalizing the notion of quadratic modules. The main theorem is a…
Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a…
We use basic tools of descriptive set theory to prove that a closed set $\mathcal S$ of marked groups has $2^{\aleph_0}$ quasi-isometry classes provided every non-empty open subset of $\mathcal S$ contains at least two non-quasi-isometric…
We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…
We introduce quasi-homomorphisms of cluster algebras, a flexible notion of a map between cluster algebras of the same type (but with different coefficients). The definition is given in terms of seed orbits, the smallest equivalence classes…
We analyze the empirical spectral distribution of random periodic band matrices with correlated entries. The correlation structure we study was first introduced in 2015 by Hochst\"attler, Kirsch and Warzel, who named their setup "almost…
Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…
A numerical semigroup is a co-finite submonoid of the monoid of non-negative integers under addition. Many properties of numerical semigroups rely on some fundamental invariants, such as, among others, the set of gaps (and its cardinality),…
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the…
A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid \Lambda we construct a C*-algebra C*(\Lambda) from it. We then present two main examples of semigroupoids, namely the Markov semigroupoid…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a…
We consider symmetric (not complete intersection) numerical semigroups S_5, generated by five elements, and derive inequalities for degrees of syzygies of S_5 and find the lower bound F_5 for their Frobenius numbers. We study a special case…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…