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Let $A = \bigoplus_{k \in \mathbb{Z}} A_k$ be a not necessarily commutative $\mathbb{Z}$-graded unital algebra over a field $\mathbb{K}$, and assume that it is strongly graded: $$ A_kA_l = A_{k+l}. $$ ...

Let $A = \oplus_{i \in \mathbb{Z}} A_i$ be a graded algebra. We say that it is strongly graded if $A_i.A_j = A_{i+j}$, for all $i,j \in \mathbb{Z}$. Can there be existing a graded algebra such that $$...

Let $k$ be an algebraically closed field of characteristic $0$. A well-known result of Lazard's states that an algebraic group which is isomorphic as a variety to an affine space is unipotent (M. ...