相关论文: Amplitude inequalities for Differential Graded mod…
We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…
Let $M$ be G-graded R-module. The idea of a graded weakly primal submodule of $M$, which is a generalization of a graded primal submodule, is introduced and discussed in this paper. Some characteristics and characterizations are assigned to…
Castelnuovo-Mumford regularity and any extended degree function can be thought of as complexity measures for the structure of finitely generated graded modules. A recent result of Doering, Gunston, Vasconcelos shows that both can be…
In this paper, we introduce the class of Cohen-Macaulay (=CM) dg (=differential graded) modules over Gorenstein dg algebras and study their basic properties. We show that the category of CM dg modules forms a Frobenius extriangulated…
We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.
For finitely generated module $M$ over a local ring $R$, the conventional notions of complete intersection dimension $\cid_R M$ and Cohen-Macaulay dimension $\cmdim_R M$ do not extend to cover the case of infinitely generated modules. In…
In this paper, we study the holonomic $D$-modules when $D$ is the ring of $k$-linear differential operators on $A = k[\Gamma]$, the coordinate ring of an affine monomial curve over the complex numbers $k = \mathbb C$. In particular, we…
We examine the cyclic homology of the monoidal category of modules over a finite dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld…
We prove that the bounded and bounded below derived categories of (all) modules over the dual numbers have strongly unique (dg) enhancements. To this end we relate those categories to the category of sequences of vector spaces, which allows…
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 $A$…
This correction article is actually unnecessary. The proof of Theorem 1.2, concerning commutative HQ-algebra spectra and commutative differential graded algebras, in the author's paper [American Journal of Mathematics vol. 129 (2007)…
We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair…
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We…
Let R be a commutative ring and M be an R-module. We define the large sum graph, denoted by \acute{G}(M), as a graph with the vertex set of non-large submodules of M and two distinct vertices are adjacent if and only if N + K is a non-large…
Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary monoidal 2-category. Examples of rigid algebras include…
Let M be a simply-connected closed manifold and consider the (ordered) configuration space of $k$ points in M, F(M,k). In this paper we construct a commutative differential graded algebra which is a potential candidate for a model of the…
The complexity of a homogeneous space $G/H$ under a reductive group $G$ is by definition the codimension of generic orbits in $G/H$ of a Borel subgroup $B\subseteq G$. We give a representation-theoretic interpretation of this number as the…
This thesis is a study of various ways of measuring the size and complexity of finitely generated modules over a Noetherian local ring. The classical example is the multiplicity or degree. Here we investigate several variants of the degree…
For a fixed finite group $Q$ and semi-simple finite dimensional algebra $S$, we examine an equivalence between strongly $Q$-graded algebras (extensions) with identity component $S$ and $S^1$-gerbes on action groupoids of $Q$ on the set of…
We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high energy symplectic homology differential and wrapped Floer homology differential in the cases of closed and open strings in a Weinstein…