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Description: |
Let $\mathbb{F}_q$ be the finite field of $q$ elements and let $A$
be an associative algebra of finite dimension over $\mathbb{F}_q$.
If the Jacobson radical is $J = J(A)$, then the set $G = 1+J$ is a
subgroup of the units of $A$ called algebra group.
\par In this work we construct the super-characters
of the algebra group $G$ for arbitrary field characteristic and we
study their main properties.
\par Finally we try to make a combinatorial description of the super-characters of $G$
when $A=\mathbb{F}_q\langle X \rangle/\mathbb{F}_q\langle X
\rangle^n$, where $\mathbb{F}_q\langle X \rangle$ is the
associative free $\mathbb{F}_q$-algebra generated by X.
Area(s):
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