Related papers: Constructing Extended Formulations from Reflection…

For a tensor ring $T_R(M)$, we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective…

We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our…

Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…

We undertake to develop a successful framework for commutative-associative hypercomplex numbers with the view to explicate and study associated geometric and generalized-relativistic concepts, basing on an interesting possibility to…

The algebra B of bicomplex numbers is viewed as a complexification of the Archimedean f-algebra of hyperbolic numbers D. This lattice-theoretic approach allows us to establish new properties of the so-called D-norms. In particular, we show…

This paper introduces an analogue of the Solomon descent algebra for the complex reflection groups of type $G(r,1,n)$. As with the Solomon descent algebra, our algebra has a basis given by sums of `distinguished' coset representatives for…

The intention of this survey to collect in one paper many recent results and advances related with Bergman type projection acting in various spaces of analytic functions in several complex variables in the unit ball, tubular domains over…

We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…

We investigate graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties) as polytopal analogues of vector spaces. In many cases we show that these retracts are again polytopal…

Laguerre and Laguerre-type polynomials are orthogonal polynomials on the interval $[0,\infty)$ with respect to a weight function of the form $w(x) = x^{\alpha} e^{-Q(x)}, Q(x) = \sum_{k=0}^m q_k x^k, \alpha > -1, q_m > 0$. The classical…

We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…

We reinterpret an inequality, due originally to Sidorenko, for linear extensions of posets in terms of convex subsets of the symmetric group $\mathfrak{S}_n$. We conjecture that the analogous inequalities hold in arbitrary…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

Let $W$ be a Coxeter group, and for $u,v\in W$, let $R_{u,v}(q)$ be the Kazhdan-Lusztig $R$-polynomial indexed by $u$ and $v$. In this paper, we present a combinatorial proof of the inversion formula on $R$-polynomials due to Kazhdan and…

An auxiliary free construction $*_{i=1}^{r}(K_i, L_i, t_i)_M$ based on HNN-extensions and on generalized free product of groups with amalgamated subgroups is suggested, and some of its basic properties are displayed. The proposed…

We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general…

We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points. To compute (with) the 0-dimensional projection and the…

We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these…