Related papers: Implication Algebras and Implication Semigroups of…

We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…

For every variety of algebras and every algebras in these variety we can consider an algebraic geometry. Algebras may be many sorted (not necessarily one sorted) algebras. A set of sorts is fixed for each variety. This theory can be applied…

We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…

This work presents a sample constructions of two algebras both with the ideal of relations defined by a finite Gr\"obner basis. For the first algebra the question whether a given element is nilpotent is algorithmically unsolvable, for the…

We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…

A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most…

(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…

Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to…

Demonic composition, demonic refinement and demonic union are alternatives to the usual "angelic" composition, angelic refinement (inclusion) and angelic (usual) union defined on binary relations. We first motivate both the angelic and…

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…

The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…

This paper continues math.GR/0608302's study of amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and applies it to graded algebras associated with finitely generated groups. Due to a…

We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…