Related papers: The Finite Basis Problem for Kauffman Monoids

We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.

We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…

We provide explicit identity bases for finite cyclic semigroups.

Let A be an alphabet and W be a set of words in the free monoid A*. Let S(W) denote the Rees quotient over the ideal of A* consisting of all words that are not subwords of words in W. We call a set of words W finitely based if the monoid…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

We provide a complete classification of matrix semirings $\mathbf{M}_n(S)$ over two-element additively idempotent semirings $S$ with respect to the finite basis property.Our main theorem shows that for every integer $n \geq 2$,the semiring…

We make a connection between the subgroup membership and identity problems for matrix groups and extended finite automata. We provide an alternative proof for the decidability of the subgroup membership problem for $ 2 \times 2 $ integer…

A variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition (A) is K-polystable unless it is contained in eight…

The polynomial-time computability of the permanent over fields of characteristic 3 for k-semi-unitary matrices (i.e. square matrices such that the differences of their Gram matrices and the corresponding identity matrices are of rank k) in…

We show that for any $N>0$ there exists a natural even $n>N$ such that the discriminant of moduli of K3 surfaces of the degree $n$ is not equal to the set of zeros of any automorphic form on the corresponding IV type domain. We give the…

The $3$-element additively idempotent semiring $S_7$ is a nonnitely based algebra of the smallest possible order. In this paper we study the nite basis problem for some additively idempotent semirings that relate to $S_7$. We present a su…

We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold $M$ is finitely generated over $\mathbb Z[A^{\pm 1}]$ if and only if $M$ is irreducible and non-Haken. We analyze in detail the character varieties $X(M)$…

We prove a generalised version of finiteness of skein modules for 3-manifolds by including boundary. We show that internal skein modules are holonomic modules over the internal skein algebra of the boundary - a property including finite…

For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $\mathcal{H}_K$,…

An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, that is, has a base for its identities consisting of 2…

Let $n>0$ be an integer and $\mathcal{X}$ be a class of groups. We say that a group $G$ satisfies the condition $(\mathcal{X},n)$ whenever in every subset with $n+1$ elements of $G$ there exist distinct elements $x,y$ such that $<x,y>$ is…

We show that there is no iterated identity satisfied by all finite groups. For $w$ being a non-trivial word of length $l$, we show that there exists a finite group $G$ of cardinality at most $\exp(l^C)$ which does not satisfy the iterated…

We show that the membership problem in a finitely generated submonoid of a graph group (also called a right-angled Artin group or a free partially commutative group) is decidable if and only if the independence graph (commutation graph) is…

We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property $\tau$. As a consequence, any closed hyperbolic 3-manifold has a co-final family…

This paper presents new results on the identities satisfied by the sylvester and Baxter monoids. We show how to embed these monoids, of any rank strictly greater than 2, into a direct product of copies of the corresponding monoid of rank 2.…