Related papers: Polytopal linear retractions
An inifinite-dimensional representation of the double affine Hecke algebra of rank 1 and type $(C_1^{\vee},C_1)$ in which all generators are tridiagonal is presented. This representation naturally leads to two systems of polynomials that…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…
We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting…
In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative…
We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…
We study a structure of the group of unitriangular automorphisms of a free associative algebra and a polynomial algebra and prove that this group is a semi direct product of abelian groups. Using this decomposition we describe a structure…
In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the…
We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…
For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the property that all interior angles between incident faces are integral submultiples of Pi, there is a naturally associated Coxeter group generated by reflections in…
Let $\g$ be a reductive Lie algebra and $V$ a $\g$-semisimple module. In this article, we study the category $\G$ of graded finite-dimensional representations of $\g \ltimes V$. We produce a large class of truncated subcategories, which are…
We study the behaviors of cohomological Hall algebras and relevant subjects under an edge contraction. Given a quiver with potential and fix an arrow, the edge contraction is a way to construct a new quiver with potential. We show that…
The aim of this work is to study the ring-theoretic properties of the diagonals of a Rees algebra, which from a geometric point of view are the homogeneous coordinate rings of embeddings of blow-ups of projective varieties along a…
We investigate a class of Lie algebras which we call {\it generalized reductive Lie algebras}. These are generalizations of semi-simple, reductive, and affine Kac-Moody Lie algebras. A generalized reductive Lie algebra which has an…
Using the braided version of Lawvere's algebraic theories and Mac Lane's PROPs, we introduce polynomial identities for arbitrary algebraic structures in a braided monoidal category C as well as their codimensions in the case when C is…
This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative algebra in an abstract monoidal model category,…
In this paper, we define a generalization of Khovanov-Lauda-Rouquier algebras which we call weighted Khovanov-Lauda-Rouquier algebras. We show that these algebras carry many of the same structures as the original Khovanov-Lauda-Rouquier…
We continue the study of twisted automorphisms of Hopf algebras started in "Twisted automorphisms of Hopf algebras". In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…
When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often…