Related papers: Subcomplexes of Certain Free Resolutions
Takiff superalgebras are a family of non semi-simple Lie superalgebras that are believed to give rise to a rich structure of indecomposable representations of associated conformal field theories. We consider the Takiff superalgebra of…
Using translation from the regular block, we construct and analyze properties of BGG complexes in singular blocks of BGG category ${\mathcal{O}}$. We provide criteria, in terms of the Kazhdan-Lusztig-Vogan polynomials, for such complexes to…
We describe a software package for constructing minimal free resolutions of GL_n(Q)-equivariant graded modules M over Q[x_1, ..., x_n] such that for all i, the ith syzygy module of M is generated in a single degree. We do so by describing…
A free resolution of free partially commutative monoids is constructed and with its help the homological dimension of these monoids is calculated.
One can iteratively obtain a free resolution of any monomial ideal $I$ by considering the mapping cone of the map of complexes associated to adding one generator at a time. Herzog and Takayama have shown that this procedure yields a minimal…
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of free resolution algorithms have been given in both cases. In this present work,…
Several spectral sequence techniques are used in order to derive information about the structure of finite free resolutions of graded modules. These results cover estimates of the minimal number of generators of defining ideals of…
We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither…
Using the Jacobi-Trudi identity as a base, we establish parallels between the theory of totally positive integer sequences and Koszul algebras. We then focus on the case of quadric hypersurface rings and use this parallel to construct new…
We find explicit free resolutions for the $\scr D$-modules ${\scr D} f^s$ and ${\scr D}[s] f^s/{\scr D}[s] f^{s+1}$, where $f$ is a reduced equation of a locally quasi-homogeneous free divisor. These results are based on the fact that every…
We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these…
We consider the notion of a connection on a module over a commutative ring, and recall the obstruction calculus for such connections. The obstruction calculus is defined using Hochschild cohomology. However, in order to compute with Grobner…
We give formulae for a module presentation of the module of identities among relations for a presentation of a group, in terms of information on 0- and 1-combings of the Cayley graph. This is seen as a special case of extending a partial…
This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its…
Let $R$ be any noetherian local ring with residue field $k$, and $A$ the homology of the Koszul complex on a minimal set of generators of the maximal ideal of $R$. In this paper, we show that a minimal free resolution of $k$ over $R$ can be…
We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring $\mathbb{F}_p[G]$ of an elementary abelian $p$-group $G$ in terms of commutative algebra. This extends results of Carlsson…
The Bershadsky-Polyakov algebras are the minimal quantum hamiltonian reductions of the affine vertex algebras associated to $\mathfrak{sl}_3$ and their simple quotients have a long history of applications in conformal field theory and…
Let $\Bbbk$ be an arbitrary field and let $b > 1, n > 1$ and $a$ be three positive integers. In this paper we explicitly describe a minimal $S-$graded free resolution of the semigroup algebra $\Bbbk[S]$ when $S$ is a generalized repunit…
The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces $\mathbb{P}^1 \times \mathbb{P}^1$, we investigate which sets…
We use the multiplicative structure of the Koszul resolution to give short and simple proofs of some known estimates for the total dimension of the cohomology of spaces which admit free torus actions and analogous results for filtered…