Related papers: Resolutions of free partially commutative monoids
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…
In this paper, we study the dimension of cohomology of semipositive line bundles over Hermitian manifolds, and obtain an asymptotic estimate for the dimension of the space of harmonic $(0,q)$-forms with values in high tensor powers of a…
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a…
We give a criterion of the semisimplicity of a p-adic unitary representation of a topological monoid by the reduction of the associated operator algebra.
We construct a canonical free resolution for arbitrary monomial modules and lattice ideals. This includes monomial ideals and defining ideals of toric varieties, and it generalizes our joint results with Irena Peeva for generic ideals.
An explicit combinatorial minimal free resolution of an arbitrary monomial ideal $I$ in a polynomial ring in $n$ variables over a field of characteristic $0$ is defined canonically, without any choices, using higher-dimensional…
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.
We provide a countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids.
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…
This paper studies the algebraic structure of a new class of hyperplane arrangement $A$ obtained by deleting two hyperplanes from a free arrangement. We provide information on the minimal free resolutions of the logarithmic derivation…
We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…
We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear…
Let $M$ be a topological monoid with homotopy group completion $\Omega BM$. Under a strong homotopy commutativity hypothesis on $M$, we show that $\pi_k (\Omega BM)$ is the quotient of the monoid of free homotopy classes $[S^k, M]$ by its…
A concrete lower-bound for the Hochschild cohomological dimension of a commutative $k$-algebra, in terms of three other homological invariants is obtained. This result is then used to show that most $k$-algebras fail to be quasi-free, even…
This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…
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…
The free regular $\star$-monoid of rank $r$ is the freest $r$-generated regular monoid $\mathbf{F}_r^\star$ in which every element $m$ has a distinguished pseudo-inverse $m^\star$ satisfying $mm^\star m = m$ and $(m^\star)^\star = m$. We…
In this paper we study the topology of the moduli spaces of representations of degree $2$ for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of $2$-dimensional representations.…
First we construct a free resolution for the Milnor (or Jacobian) algebra $M(f)$ of a complex projective Chebyshev plane curve $\CC_d:f=0$ of degree $d$. In particular, this resolution implies that the dimensions of the graded components…
Transformations of coherent states of the free particle by bounded and semibounded symmetry operators are considered. Resolution of the identity operator in terms of the transformed states is analyzed. A generalized identity resolution is…