Related papers: Cellular $E_k$-algebras
In this article we study the representations of general linear groups which arise from their action on flag spaces. These representations can be decomposed into irreducibles by proving that the associated Hecke algebra is cellular. We give…
We consider the $ r = 0 $ case of the conjectures by Bonnaf\'e, Geck, Iancu and Lam on cellular structures on the Hecke algebra of type $ B $. We show that this case induces the natural cell structure on the blob algebra $ b_n $ by…
This paper provides a systematization of some recent results in homology of algebras. Our main theorem gives criteria under which the homology of a diagram algebra is isomorphic to the homology of the subalgebra on diagrams having the…
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of…
We study the congeniality property of algebras, as defined by Bao, He, and Zhang, in order to establish a version of Auslander's theorem for various families of filtered algebras. It is shown that the property is preserved under homomorphic…
In this paper we describe several characterizations of basic finite-dimensional $k$-algebras $A$ stratified for all linear orders, and classify their graded algebras as tensor algebras satisfying some extra property. We also discuss whether…
We construct, using finitely many generating cell and relations, props in the category of CW-complexes with the property that their associated operads are models for the $E_\infty$-operad. We use one of these to construct a cellular…
We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…
We prove some stability results for certain classes of C*-algebras. We prove that whenever $A$ is a finite-dimensional C*-algebra, $B$ is a C*-algebra and $\phi\colon A\to B$ is approximately a $^*$-homomorphism then there is an actual…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
In this paper, we realize the algebra of $\mathbb{Z}_2$-relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of \cite{GM1}. Using the results of Graham…
We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the…
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological…
Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict…
We develop the homological theory of KLR algebras of symmetric affine type. For each PBW basis, a family of standard modules is constructed which categorifies the PBW basis.
We show how the treatment of cellularity in families of algebras arising from diagram calculi, such as Jones' Temperley--Lieb wreaths, variants on Brauer's centralizer algebras, and the contour algebras of Cox et al (of which many algebras…
For simply-laced quivers, we consider the fixed-point subalgebra of the quiver Hecke algebra under the homogeneous sign map. This leads to a new family of algebras we call alternating quiver Hecke algebras. We give a basis theorem and a…