Related papers: A remark on Rickard complexes

We introduce the periplectic $q$-Brauer category over an integral domain of characteristic not $2$. This is a strict monoidal supercategory and can be considered as a $q$-analogue of the periplectic Brauer category. We prove that the…

Let $n$ be a positive integer and $q$ a prime power. We prove that a refined version of Brou\'{e}'s abelian defect group conjecture holds for unipotent $\ell$-blocks of ${\rm GL}_n(q)$, where $\ell\nmid q$. We also give a sufficient…

We prove that every Ariki-Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki-Koike algebras which have q-connected parameter sets. A similar result is proved for the cyclotomic q-Schur algebras. Combining…

In this paper, we study in the context of quantum vertex algebras a certain Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW type and classify its $\mathbb N$-graded irreducible modules by using a notion of Verma…

We define weak 2-categories of finite dimensional algebras with bimodules, along with collections of operators $\mathbb{O}_{(c,x)}$ on these 2-categories. We prove that special examples $\mathbb{O}_p$ of these operators control all…

We define and study RoCK blocks for double covers of symmetric groups. We prove that RoCK blocks of double covers are Morita equivalent to standard `local' blocks. The analogous result for blocks of symmetric groups, a theorem of Chuang and…

We introduce a new class of symmetric algebras, which we call hybrid algebras. This class contains on one extreme Brauer graph algebras, and on the other extreme general weighted surface algebras. We show that hybrid algebras are precisely…

A well-known result of Scopes states that there are only finitely many Morita equivalence classes of $p$-blocks of symmetric groups with a given weight (or defect). In this note we investigate a lower bound on the number of those Morita…

Rook-Brauer algebras are a family of diagram algebras. They contain many interesting subalgebras: rook algebras, Brauer algebras, Motzkin algebras, Temperley-Lieb algebras and symmetric group algebras. In this paper, we generalize the…

A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing completely pointless objects. All…

Let $X$ be a smooth proper curve defined over a field $k$. The representability of the relative Picard functor is obstructed by a class $\alpha\in\mathrm{Br}(\mathrm{Pic}_{X/k})$. We show the associated division algebra on…

We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of…

We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of…

We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…

The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison…

Let $Q$ be an acyclic quiver. Associated with any element $w$ of the Coxeter group of $Q$, triangulated categories $\underline{\Sub}\Lambda_w$ were introduced in \cite{Bua2}. There are shown to be triangle equivalent to generalized cluster…

A set of valuable universal similarity factorization equalities is established over complex Clifford algebras $\Cn.$ Through them matrix representations of complex Clifford algebras $\Cn$ can directly be derived, and their properties can…

In this paper, we determine the cocycle deformations and Galois objects for semisimple Hopf algebras of dimension pqr, and decide the categorically Morita equivalent classes and monoidally Morita equivalent classes of them. We show that all…

We provide a direct proof that the Hochschild homology of a $\mathbb{Z}_2$-graded algebra is Morita invariant.

We construct families of differential graded algebras R and R \boxtimes R and give an algebraic formulation of the contact category of a disk through the differential graded category DGP(R) generated by some distinguished projective…