Related papers: Graded Algebras, Algebraic Functions, Planar Trees…

Given an ideal of forms in an algebra (polynomial ring, tensor algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we consider the Hilbert series of the factor ring. We concentrate on the minimal Hilbert series, which is…

It is well known that algebraic power series are differentially finite (D-finite): they satisfy linear differential equations with polynomial coefficients. The converse problem, whether a given D-finite power series is algebraic or…

We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.

We compute the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an $\operatorname{SU}_2$-module and give an explicit expression for the first nonzero coefficient of the Laurent…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

We associate to each $r$-multigraded, locally finitely generated ideal in the "large polynomial ring" on countably many indeterminates a power series in $r$ variables; this power series is the limit in the adic topology of the numerators of…

In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the…

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the term graded is applied to non-negatively…

We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In…

We present a functorial construction which, starting from a congruence $\alpha$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences…

An algebra A with a generalized H-action is a generalization of an H-module algebra where H is just an associative algebra with 1 and a relaxed compatibility condition between the multiplication in A and the H-action on A holds. At first…

Motivated by results on the rationality of equivariant Hilbert series of some hierarchical models in algebraic statistics we introduce the Segre product of formal languages and apply it to establish rationality of equivariant Hilbert series…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

The structure of Lie algebras, Lie superalgebras and Leibniz algebras graded by finite root systems has been studied by several researchers since 1992. In this paper, we study the structure of Leibniz superalgebras graded by finite root…

We study generalized symbolic powers and form ideals of powers of ideals and compare their growth with the growth of ordinary powers, and we discuss the question of when the graded rings attached to symbolic powers or to form ideals of…

Let $k$ be a field and let $A=\bigoplus_{n\ge 1}A_n$ be a positively graded $k$-algebra. We recall that $A$ is graded nilpotent if for every $d\ge 1$, the subalgebra of $A$ generated by elements of degree $d$ is nilpotent. We give a method…

This paper continues the work which attempts to understand the general properties of the graded algebras associated with Hecke symmetries without a restriction on the parameter q of the Hecke relation imposed in earlier results.

We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…

We study the Hilbert function and the graded Betti numbers of almost complete intersection artinian algebras. We show that that every Hilbert function of a complete intersection artinian algebra is the Hilbert function of an almost complete…