Related papers: Resolutions for Truncated Ore Extensions

We introduce a new method of constructing complete sequences of key polynomials for simple extensions of tame fields. In our approach the key polynomials are taken to be the minimal polynomials over the base field of suitably constructed…

We present a graded-geometric approach to modular classes of Lie algebroids and their generalizations, introducing in this setting an idea of relative modular class of a Dirac structure for a certain type of Courant algebroids, called…

In the paper, we investigate the lifting of recollements with respect to Gorenstein-projective modules. Specifically, a homological ring epimorphism can induce a lifting of the recollement of the stable category of finitely generated…

Let $\mathbb{F}$ be a division ring. In this paper, we extent some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension $\mathbb{F}[x;\sigma,\delta]$. Finally, some…

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

This paper shows among other things that over a non-commutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions.

Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…

We study equivariant modules over $GL(V)$ over the polynomial ring $R = Sym V$. We introduce for every partition $\lambda$ the elementary equivariant module $M_{\lambda}$. Then we prove that any finitely generated equivariant module admits…

The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl…

Let k be a commutative ring. We find and characterize a new family of twisted planes (i. e. associative unitary k-algebra structures on the k-module k[X,Y], having k[X] and and k[Y] as subalgebras).Similar results are obtained for the…

In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain integer sequences. Moreover, we give an algorithm to construct…

We construct a family of PL triangulations of the $d$-dimensional real projective space $\mathbb{R}P^d$ on $\Theta((\frac{1+\sqrt{5}}{2})^{d+1})$ vertices for every $d\geq 1$. This improves a construction due to K\"{u}hnel on $2^{d+1}-1$…

We derive a formula for the the modular class of a Lie algebroid with a regular twisted Poisson structure in terms of a canonical Lie algebroid representation of the image of the Poisson map. We use this formula to compute the modular…

We obtain improved Fourier restriction estimate for the truncated cone using the method of polynomial partitioning in dimension $n\geq 3$, which in particular solves the cone restriction conjecture for $n=5$, and recovers the sharp range…

In this paper, we study the uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials.

We show how to extract alternative solutions for optimization problems solved by Benders Decomposition. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative…

Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…

Let $V$ be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the…