Thick Subcategories of the stable category of modules over the exterior algebra
We study thick subcategories defined by modules of complexity one in $\underline{\md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.
math.RT↗
arXiv subjects
Dan Zacharia
Publications and source records attributed to Dan Zacharia.
On the diagonal subalgebra of an Ext algebra
Let $R$ be a Koszul algebra over a field $k$ and $M$ be a linear $R$-module. We study a graded subalgebra $Δ_M$ of the Ext-algebra $\operatorname{Ext}_R^*(M,M)$ called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of $R$ and to periodicity of linear modules are given. Viewing $R$ as a linear module over its enveloping algebra, we also show that $Δ_R$ is isomorphic to the graded center of the Koszul dual of $R$.
math.KT↗
Algebras of finite global dimension
Let $Λ$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
math.RT↗
A note on sheaves without self-extensions on the projective $n$-space
Let ${\bf P}^n$ be the projective $n-$space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on ${\bf P}^n$ has a trivial endomorphism algebra. This generalizes a result of Drezet for $n=2.$
math.AG↗