Now showing items 1-5 of 5

• #### Cataland: Why the Fuß? ﻿

[OWP-2019-01] (Mathematisches Forschungsinstitut Oberwolfach, 2019-01-21)
The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. ...
• #### The First Hochschild Cohomology as a Lie Algebra ﻿

[OWP-2019-09] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-16)
In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, ...
• #### Group-Graded Rings Satisfying the Strong Rank Condition ﻿

[OWP-2019-22] (Mathematisches Forschungsinstitut Oberwolfach, 2019-08-16)
A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ...
• #### On the Lie Algebra Structure of $HH^1(A)$ of a Finite-Dimensional Algebra A ﻿

[OWP-2019-10] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-17)
Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ...
• #### Weighted Surface Algebras: General Version ﻿

[OWP-2019-07] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-28)
We introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, ...