Related papers: On the algebraic structure of differentially homog…
We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by…
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 $a(t)$…
It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous…
We present a complete algebraic description of the field of first-order joint projective invariants for configurations of \( n \) points in the plane, under the natural diagonal action of the projective group \( PGL(3,\mathbb{R}) \). For \(…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
We prove that, if $A$ is a positively graded, graded commutative, local, finite Hopf algebra, its cohomology is finitely generated, thus unifying classical results of Wilkerson and Hopkins-Smith, and of Friedlander-Suslin. We do this by…
We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…
In this paper, we establish a structure theorem for connected graded Hopf algebras over a field of characteristic $0$ by claiming the existence of a family of homogeneous generators and a total order on the index set that satisfy some…
A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We…
The literature in persistent homology often refers to a "structure theorem for finitely generated graded modules over a graded principal ideal domain". We clarify the nature of this structure theorem in this context.
We formulate the generation of finite dimensional pointed Hopf algebras by group-like elements and skew-primitives in geometric terms. This is done through a more general study of connected and coconnected Hopf algebras inside a braided…
In this short note we study the cohomology algebra of saturated fusion systems using finite groups which realize saturated fusion systems and Hochschild cohomology of group algebras. A similar result to a theorem of Alperin is proved for…
We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…
It is shown that every $2$-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra $A$ defines a very explicit infinitesimal $2$-braiding on the homotopy $2$-category of the symmetric monoidal…
Using recent work by Erman-Sam-Snowden, we show that finitely generated ideals in the ring of bounded-degree formal power series in infinitely many variables have finitely generated Gr\"obner bases relative to the graded reverse…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
Let $G$ be the linear algebraic group $SL_3$ over a field $k$ of characteristic two. Let $A$ be a finitely generated commutative $k$-algebra on which $G$ acts rationally by $k$-algebra automorphisms. We show that the full cohomology ring…
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…
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 develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several questions, e.g. the notion of homological unit…