Related papers: Finitely generated equational classes
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many…
We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also…
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 expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…
We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an "extremal" relation, i.e. the identity or the universal relation. The corresponding logics have…
We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right) orderable groups. This answers a well known open question…
It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can…
It has been conjectured that finite tensor categories have finitely generated cohomology. We show that this is equivalent to finitely generated Hochschild cohomology for the endomorphism algebras of the projective generators.
We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…
In this paper, we prove that uniformly bounded simple Lie conformal algebra must be finitely generated. Furthermore, we give a completely classification of simple uniformly bounded Lie conformal algebras with upper bound one.
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
A tubular group $G$ is a finite graph of groups with $\mathbb{Z}^2$ vertex groups and $\mathbb{Z}$ edge groups. We characterize residually finite tubular groups: $G$ is residually finite if and only if its edge groups are separable. Methods…
Let $k$ be a perfect field such that for every $n$ there are only finitely many field extensions, up to isomorphism, of $k$ of degree $n$. If $G$ is a reductive algebraic group defined over $k$, whose characteristic is very good for $G$,…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
In this paper, we prove the following characterization: an abelian Mal'cev variety is finitely based if and only it has finite type, its ring of idempotent binary terms is finitely presented, and its module of unary terms is finitely…
In the affine fragment of continuous logic, type spaces are compact convex sets. I study some model theoretic properties of extreme types. It is proved that every complete theory $T$ has an extremal model, i.e. a model which realizes only…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…