Abstract We give a combinatorial characterization of amenability monomial algebras and prove the existence Følner sequences, answering question due to Ceccherini–Silberstein Samet–Vaillant. then use our that over projectively simple algebras, every module is exhaustively amenable; we conclude convolution minimal subshifts admit same property. deduce any subshift positive entropy gives rise grad...

In this paper we derive an explicit version of the BernsteinGel’fand-Gel’fand (BGG) correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite free resolutions over its “Koszul dual” exterior algebra. Among the facts about the BGG correspondence that we derive is that taking homology of a complex of sheaves corresponds to taking the “linear part...

Let K be a field with char(K)=0. For partition λ of n∈N, let IλSp the ideal R=K[x1,…,xn] generated by all Specht polynomials shape λ. These ideals have been studied from several points view (and under names). Using advanced tools representation theory, Berkesch Zamaere et al. [1] constructed minimal free resolution I(n−d,d)Sp except differential maps. The present paper constructs maps, and also...

in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. ...

Let U ⊆ H(OP1×P1 (2, 1)) be a basepoint free four-dimensional vector space. The sections corresponding to U determine a regular map φU : P1 × P1 −→ P3. We study the associated bigraded ideal IU ⊆ k[s, t;u, v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determinin...

In this paper we prove an analogue of a recent result of Gordon and Stafford that relates the representation theory of certain noncommutative deformations of the coordinate ring of the nth symmetric power of C2 with the geometry of the Hilbert scheme of n points in C2 through the formalism of Z-algebras. Our work produces, for every regular noncommutative deformation Oλ of a Kleinian singularit...

For a radical monomial ideal I in a normal semigroup ring k[Q], there is a unique minimal irreducible resolution 0 → k[Q]/I → W 0 → W 1 → · · · by modules W i of the form ⊕ j k[Fij ], where the Fij are (not necessarily distinct) faces of Q. That is, W i is a direct sum of quotients of k[Q] by prime ideals. This paper characterizes Cohen–Macaulay quotients k[Q]/I as those whose minimal irreducib...