Related papers: Finitely generated free Heyting algebras via Birkh…
For every $n \in \mathbb{N}$, we construct a variety of Heyting algebras, whose $n$-generated free algebra is finite but whose $(n+1)$-generated free algebra is infinite.
In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hilbert series of an associative algebra. Namely, we construct…
It is known that exactly eight varieties of Heyting algebras have a model-completion, but no concrete axiomatisation of these model-completions were known by now except for the trivial variety (reduced to the one-point algebra) and the…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the…
For any $n<\omega$ we construct an infinite Heyting algebra $H_n$ which is $(n+1)$-generated but that contains only finite $n$-generated subalgebras. From this we conclude that for every $n<\omega$ there exists a variety of Heyting algebras…
We prove that there exist profinite Heyting algebras that are not isomorphic to the profinite completion of any Heyting algebra. This resolves an open problem from 2009. More generally, we characterize those varieties of Heyting algebras in…
Given a finitely generated free monoid $X$ and a morphism $\phi : X\to X$, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras…
Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
We consider absolutely free nonassociative algebras and, more generally, absolutely free algebras with (maybe infinitely) many multilinear operations. Such algebras are described in terms of labeled reduced planar rooted trees. This allows…
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…
For any power series $a(t)$ with exponentially bounded nonnegative integer coefficients we suggest a simple construction of a finitely generated monomial associative algebra $R$ with Hilbert series $H(R,t)$ very close to $a(t)$. If $a(t)$…
This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…
We prove that the cohomology algebra of a conilpotent Lie coalgebra is generated in degree 1 as an A-infinity algebra. By dualizing, the same is true about cohomology algebras of finite dimensional nilpotent Lie algebras. In the process, we…
Given a simple vertex algebra A and a reductive group G of automorphisms of A, the invariant subalgebra A^G is strongly finitely generated in most examples where its structure is known. This phenomenon is subtle, and is generally not true…
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…
Ruitenburg's Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ultimately periodic if f fixes all the generators but one. More precisely, there is N $\ge$ 0 such that f N +2 = f N , thus the period…
We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categories.