Related papers: A note on specializing semi-orthogonal decompositi…
We show that the bounded derived category of coherent sheaves on a smooth projective curve except the projective line admits no non-trivial semi-orthogonal decompositions.
This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.
In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson…
In this letter, first, we prove that the orthonormal basis of rational Littlewood-Paley wavelet with rational dilation factor M=p/q first proposed by Auscher does not hold for all rational numbers. It does not hold if q is not equal to 1.…
We provide algorithmic methods to check the Cohen--Macaulayness, Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are constructed from the dilation of bounded convex polyhedrons of $\R^3_{\geq}$. Some families of…
In the present paper we derive complicated families of orthogonal polynomials in one variable from scratch using the known ones as building blocks. We recall the basics of operational formalism and introduce the notations we use throughout…
We construct $S$-linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations $X/S$ with relative Picard rank $1$ and rational geometric fibers and discuss how the structure of components of these…
Unfortunately, some proofs in the first version of this paper were incorrect. In this revised version, some minor gaps are fixed, one serious mistake found. The main theorem is now claimed only under a restrictive technical assumption. This…
A computation shows that there are 77 (up to scalar shifts) possible pairs of integer coefficient polynomials of degree five, having roots of unity as their roots, and satisfying the conditions of Beukers and Heckman [1], so that the…
Let $R$ be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over $R$. Additionally, we study orthogonal decompositions…
Several important families of orthogonal polynomials on the real line are called ``hypergeometric'' since they can be explicitly described in terms of some hypergeometric series $_pF_q$ that uses the degree $n$ of the polynomial as a…
It is shown that the Hochschild Cohomological dimension of an associative algebra is not an upper-semi continuous function, showing the semi-continuity theorem is no longer valid for non-commutative algebras. A family of $\mathbb{C}$…
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…
In a classical case, orthogonal polynomial sequences are in such a way that the $ n $th polynomial has the exact degree $n$. Such sequences are complete and form a basis of the space for any arbitrary polynomial. In this paper, we introduce…
Let U be the tautological subbundle on the Grassmannian $\mathrm{Gr}(k, n)$. There is a natural morphism $\mathrm{Tot}(U) \to \mathbb{A}^n$. Using it, we give a semiorthogonal decomposition for the bounded derived category…
We extend the notion of semi-infinite cohomology of Lie algebras to include cases where the Lie algebra does not admit a semi-infinite structure but satisfies a mild condition. Our construction clarifies the definition of affine W-algebras…
We construct a family of $(2,n)$-almost Grassmannian structures of regularity $C^1$, each admitting a one-parameter group of strongly essential automorphisms, and each not flat on any neighborhood of the higher-order fixed point. This shows…
In [1] we highlighted the fact that the log polynomial expansion employed in Nature Astron. 3, no.3, 272-277 (2019) [2] is a poor approximation to flat $\Lambda$CDM, so using it to infer deviations from flat $\Lambda$CDM is not…
Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.