相关论文: Morita equivalences between cyclotomic KLR algebra…

This paper is investigative work into the properties of a family of graded algebras recently defined by Varagnolo and Vasserot, which we call VV algebras. We compare categories of modules over KLR algebras with categories of modules over VV…

This note uses a variation of graded Morita theory for finite dimensional superalgebras to determine explicitly the graded basic superalgebras for all real and complex Clifford superalgebras. As an application, the Grothendieck groups of…

We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite…

We classify the rational Cherednik algebras H_c(W) (and their spherical subalgebras) up to isomorphism and Morita equivalence in case when W is the symmetric group and `c' is a generic parameter value.

We show some properties on a special case of level 1 cyclotomic KLR algebras of type $A_{n}^{(1)}$; the number of primitive idempotents, systematic change of structures, the dimension.

We prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether every Exel-Laca algebra is Morita equivalent to a…

This paper shows that the cyclotomic quiver Hecke algebras of type $A$, and the gradings on these algebras, are intimately related to the classical seminormal forms. We start by classifying all seminormal bases and then give an explicit…

We provide a complete classification of the class of unital graph $C^*$-algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalence in this case is determined by ordered, filtered…

Weighted KLRW algebras are diagram algebras generalizing KLR algebras. This paper undertakes a systematic study of these algebras culminating in the construction of homogeneous affine cellular bases in affine types A and C, which…

We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type C. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we…

We take another look at the construction of double $\infty$-categories of algebras and bimodules and prove a few supplemental results about these, including a simpler proof of the Segal condition and a comparison between our construction…

We give a Morita equivalence theorem for so-called cyclotomic quotients of affine Hecke algebras of type B and D, in the spirit of a classical result of Dipper-Mathas in type A for Ariki-Koike algebras. As a consequence, the representation…

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…

We introduce Morita equivalence to the study of Kleene algebras and modules. Classical characterizations of Morita-equivalent semirings such as having equivalent categories of modules and one semiring being a full matrix algebra over the…

We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C. We prove that two…

In this paper we introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate some properties of the new version of Morita…

In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras

We call an $\mathbb{R}$-algebra locally complexified-gentle if it becomes a locally gentle $\mathbb{C}$-algebra up to Morita equivalence after complexification. We use modulated quivers to introduce two types of locally complexified-gentle…

This paper initiates a systematic study of the cyclotomic KLR algebras of affine types $A$ and $C$. We start by introducing a graded deformation of these algebras and the constructing all of the irreducible representations of the deformed…

We use the technology of linking groupoids to show that equivalent groupoids have Morita equivalent reduced C*-algebras. This equivalence is compatible in a natural way in with the Equivalence Theorem for full groupoid C*-algebras.