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We rule out a certain $9$-dimensional algebra over an algebraically closed field to be the basic algebra of a block of a finite group, thereby completing the classification of basic algebras of dimension at most $12$ of blocks of finite group algebras.
We show that there is a simple separable unital (non-nuclear) tracially AF algebra $A$ which does not absorb the Jiang-Su algebra $mathcal Z$ tensorially, i.e., $A cong Aotimesmathcal Z$.
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. The second main result shows t
We prove that if $B$ is a $p$-block with non-trivial defect group $D$ of a finite $p$-solvable group $G$, then $ell(B) < p^r$, where $r$ is the sectional rank of $D$. We remark that there are infinitely many $p$-blocks $B$ with non-Abelian defect gro
Let $L$ be a Lie algebra of Block type over $C$ with basis ${L_{alpha,i},|,alpha,iinZ}$ and brackets $[L_{alpha,i},L_{beta,j}]=(beta(i+1)-alpha(j+1))L_{alpha+beta,i+j}$. In this paper, we shall construct a formal distribution Lie algebra of $L$. Then
We show that if $B$ is a block of a finite group algebra $kG$ over an algebraically closed field $k$ of prime characteristic $p$ such that $HH^1(B)$ is a simple Lie algebra and such that $B$ has a unique isomorphism class of simple modules, then $B$