Related papers: Representations of relatively free profinite semig…
If the Krull dimension of the semigroup ring is greater than one, then affine semigroups of maximal projective dimension ($\mathrm{MPD}$) are not Cohen-Macaulay, but they may be Buchsbaum. We give a necessary and sufficient condition for…
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…
Takahasi's theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of periodic points are finitely generated and periodic orbits…
We investigate the complexity of deciding, given a multiplication table representing a semigroup S, a subset X of S and an element t of S, whether t can be expressed as a product of elements of X. It is well-known that this problem is…
By the planarity rank of a semigroup variety we mean the largest number of generators of a free semigroup of a variety with respect to which the semigroup admits a planar Cayley graph. Since the time when L.M.Martynov formulated the problem…
We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson's group $F$ which is strictly well-ordered by the embeddability relation in type $\epsilon_0 +1$. All except the maximum element of this family…
We present obstruction results for self-similar groups regarding the generation of free groups. As a main consequence of our main results, we solve an open problem posed by Grigorchuk by showing that in an automaton group where a…
We study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially ordered abelian group G is finitely presented if and only…
As an instance of a linear action of a Hopf algebra on a free associative algebra, we consider finite group gradings of a free algebra induced by gradings on the space spanned by the free generators. The homogeneous component corresponding…
We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central…
The 5-element Brandt semigroup $B_2$ admits the structure of a naturally semilattice-ordered inverse semigroup, thus becoming an additively idempotent semiring with the operation of taking greatest lower bounds as the semiring addition. For…
We prove the following three closely related results. The first is that every finite simple group has a profinite presentation with 2 generators and at most 18 relations. The second is that if G is a finite simple group, F a field and M an…
For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions…
Primitive representations of finite groups as well as primitive finite groups were classified in the O'Nan-Scott Theorem. In this paper we classify faithful finite primitive semigroup representations. To each finite primitive…
Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on…
In this article, we study the elements with disconnected centralizer in the Brauer complex associated to a simple algebraic group G defined over a finite field with corresponding Frobenius map F and derive the number of F-stable semisimple…
This paper continues the functional approach to the P-versus-NP problem, begun in [1]. Here we focus on the monoid RM_2^P of right-ideal morphisms of the free monoid, that have polynomial input balance and polynomial time-complexity. We…
We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.
In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \cite{Kosh, can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally…