We introduce the notion of mutation on the set of n-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

We study cluster tilting modules in mesh algebras of Dynkin type as defined [12], providing a new proof for their existence. Except G2, we show that these are precisely the maximal rigid modules, and they equivariant certain automorphism. further mutation, an example mutation abelian category which is not stably 2-Calabi-Yau, explicitly describe combinatorics.

We study Serre’s condition (Sn) for tensor products of modules over a commutative noetherian local ring R. Specifically, we consider the following question. For finitely generated R-modules M and N, either which is (n+1)-Tor-rigid, if product M⊗RN satisfies (Sn+1), then does ToriR(M,N)=0 hold all i≥1? The aim this paper to give an affirmative answer question assume freeness on modules. As appli...

We introduce the notion of mutation on the set of n-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

We compute the representation-theoretic rank of a finite dimensional quasi-Hopf algebra H and of its quantum double D(H), within the rigid braided category of finite dimensional left D(H)-modules.

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

We consider stacks of filtered φ-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrising integral data and de...

We study structure, eigenvalue spectra, and random-walk dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adj...