Related papers: Algebras and their Associated Monomial Algebras

The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…

Associated to any uniform finite layered graph Gamma there is a noncommutative graded quadratic algebra A(Gamma) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul.…

We show that every strongly $\mathbb{Z}$-graded C*-algebra (equivalently, every C*-algebra carrying a strongly continuous $\mathbb{T}$-action with full spectral subspaces) is a Cuntz--Pimsner algebra, and describe subalgebras and subspaces…

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A = kQ/I. Let QGr A denote…

In this paper we construct non-negative gradings on a basic Brauer tree algebra $A_{\Gamma}$ corresponding to an arbitrary Brauer tree $\Gamma$ of type $(m,e)$. We do this by transferring gradings via derived equivalence from a basic Brauer…

The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…

We study algebras k[x_1,...,x_n]/I which admit a grading by a subsemigroup of N^d such that every graded component is a one-dimensional k-vector space. V.I.~Arnold and coworkers proved that for d = 1 and n <= 3 there are only finitely many…

Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive…

On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra, A…

We consider rational power series over an alphabet $\Sigma$ with coefficients in a ordered commutative semiring $K$ and characterize them as the free ordered $K$-semialgebras in various classes of ordered $K$-semialgebras equipped with a…

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…

Let $G$ be a finite abelian group and let $K$ be an algebraically closed field of characteristic 0. We consider associative unital algebras $A$ over $K$ graded by $G$, that is $A=\oplus_{g\in G} A_g$, where the vector subspaces $A_g$…

Let $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\GG(A)$ of $A$ is generated by monomials of degree $(r-1)d$ in $S$. We…

The purpose of this paper is to study generalizations of Gamma-homology in the context of operads. Good homology theories are associated to operads under appropriate cofibrancy hypotheses, but this requirement is not satisfied by usual…

In this paper we introduce an algebra embedding $\iota:K< X >\to S$ from the free associative algebra $K< X >$ generated by a finite or countable set $X$ into the skew monoid ring $S = P * \Sigma$ defined by the commutative polynomial ring…

Consider a height two ideal, $I$, which is minimally generated by $m$ homogeneous forms of degree $d$ in the polynomial ring $R=k[x,y]$. Suppose that one column in the homogeneous presenting matrix $\f$ of $I$ has entries of degree $n$ and…

We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…

In this article we define $G$-algebras, that is, graded algebras on which a reductive group $G$ acts as gradation preserving automorphisms. Starting from a finite dimensional $G$-module $V$ and the polynomial ring $\mathbb{C}[V]$, it is…

We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$…

Let $G$ be a simple graph on $d$ vertices. We define a monomial ideal $K$ in the Stanley-Reisner ring $A$ of the order complex of the Boolean algebra on $d$ atoms. The monomials in $K$ are in one-to-one correspondence with the proper…