Semisimple algebras and PI-invariants of finite dimensional algebras

dimensional Grassmann algebra and $E(A)$ is the Grassmann envelope of $A$. [6/6 of https://t.co/NVTef9ayU1]

if $A$ and $B$ are finite dimensional $G_{2}:= \mathbb{Z}_{2} \times G$-graded simple algebras then they are $G_{2}$-graded isomorphic if and only if $E(A)$ and $E(B)$ are $G$-graded PI-equivalent, where $E$ is the unital infinite [5/6 of https://t.co/NVTe

direct summand of $B_{ss}$. We refer to $U$ as the unique minimal semisimple algebra corresponding to $\Gamma$. We fully extend this result to the non-affine $G$-graded setting where $G$ is a finite group. In particular we show that [4/6 of https://t.co/NV

Wedderburn-Malcev decomposition $A \cong U \oplus J_{A}$, where $J_{A}$ is the Jacobson's radical of $A$ $(2)$ If $B \in \mathcal{M}_{\Gamma}$ and $B \cong B_{ss} \oplus J_{B}$ is its Wedderburn-Malcev decomposition then $U$ is a [3/6 of https://t.co/NVTef