Related papers: Simple connectedness of quasitilted algebras

This paper investigates if a differential graded algebra can have more than one $A_\infty$-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an $A_\infty$-structure up…

Let $G$ be a split connected reductive group over $\mathbb{Z}$. Let $F$ be a non-archimedean local field. With $K_m: = Ker(G(\mathfrak{O}_F) \rightarrow G(\mathfrak{O}_F/\mathfrak{p}_F^m))$, Kazhdan proved that for a field $F'$sufficiently…

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra…

In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for…

Let g be a complex, semisimple Lie algebra, G the corresponding simply-connected Lie group and H a maximal torus in G. We construct a flat connection on H with logarithmic singularities on the root hypertori and values in the Yangian Y(g)…

It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial)…

We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear…

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, and $M$ be a partial tilting $A$-module. We prove that the Bongartz $\tau$-tilting complement of $M$ coincides with its Bongartz complement, and then we give a…

We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the periodicity group of the graph. The groupoid…

Let G be a connected, simply connected, simple complex algebraic group and let e be a primitive l-th root of 1, with l odd and 3 does not divide l if G is of type G_{2}. We determine all Hopf algebra quotients of the quantized coordinate…

Using the recent advancements in the structure of algebraic groups over imperfect fields, we propose a generalization of Serre's Conjecture I and of results that revolve around it. In particular, we prove that the first Galois cohomology…

This is the geometric part of two papers on the cohomology of Kaehler groups. Using non-Abelian Hodge theory we show that if a finitely presented group with an unbounded complex linear morphism is the fundamental group of a compact Kaehler…

Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$ are investigated. In particular, all Lie bialgebra structures on $\widetilde{sl_2(\mathbb{C}_q)}$ are shown to be triangular coboundary. This…

We show that if $A$ is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of $A$ is quasiconvex. In particular, closed sets which are null sets for the cc-Hausdorff $3$-measure have…

Braided algebras are associative algebras endowed with a Yang-Baxter operator that satisfies certain compatibility conditions involving the multiplication. Along with Hochschild cohomology of algebras, there is also a notion of Yang-Baxter…

We characterize the solvable Lie groups of the form ${\mathbb R}^m\rtimes {\mathbb R}$, whose $C^*$-algebras are quasidiagonal. Using this result, we determine the connected simply connected solvable Lie groups of type~I whose…

We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…

We prove that the Heisenberg groups can be distinguished from the other connected and simply connected Lie groups via their group $C^*$-algebras. The main step of the proof is a characterization of the nilpotent Lie groups among the…

Let g be a complex, semisimple Lie algebra. We prove the existence of a quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping algebra of g, which binds the quasi-Coxeter structure underlying the Casimir connection of g…