Related papers: Tilting Modules over Tame Hereditary Algebras

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

For a finite dimensional algebra $\Lambda$ and a non-negative integer $n$, we characterize when the set $\tilt_n\Lambda$ of additive equivalence classes of tilting modules with projective dimension at most $n$ has a minimal (or…

This work concerns finite free complexes with finite length homology over a commutative noetherian local ring $R$. The focus is on complexes that have length $\mathrm{dim}\, R$, which is the smallest possible value, and in particular on…

The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain…

The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects $T$ in cluster categories; we call such an algebra cluster-concealed in case $T$ is obtained from a…

We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that…

We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to deduce a criterion for an exact functor between two affine…

Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

Let $F$ be a finite extension of $\mathbb{Q}_p$. Let $W(k)$ denote the Witt vectors of an algebraically closed field $k$ of characteristic $\ell$ different from $p$ and $2$, and let $\mathcal{Z}$ be the spherical Hecke algebra for $GL_n(F)$…

We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.

The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated.…

We show that all finite dimensional, tame hereditary $k$-algebras are of amenable representation type (in the sense of G. Elek) for all fields $k$. The proof is adapted from our previous result for tame path algebras. Further, it is proven…

The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module direct images from the torus to the base space through orbits…

In the first part of this paper the projective dimension of the structural modules in the BGG category $\mathcal{O}$ is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an…

We show that indecomposable exact module categories over the category Rep H of representations of a finite-dimensional Hopf algebra H are classified by left comodule algebras, H-simple from the right and with trivial coinvariants, up to…

We consider a finite dimensional strongly $G$-graded algebra $A$ with { self-injective} $1$-component $B$, and in our main result we prove that the induction from $B$ to $A$ of a basic support $\tau$-tilting pair of $B$-modules is a support…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of…

We study Tate-Vogel and relative cohomologies of complexes by applying the model structure induced by a complete hereditary cotorsion pair ($\A$, $\B$) of modules. We show first that the class of complexes admitting a complete $\A$…