Automorphisms of the semigroup of endomorphisms of free associative algebras

Details Automorphisms of the semigroup of endomorphisms of free associative algebras Automorphisms of the semigroup of endomorphisms of free associative algebras

2005-12-13

arxiv.org/abs/math/0512273v3

Mathematics

Rings and Algebras

Scientific paper

Let $A=A(x_{1},...,x_{n})$ be a free associative algebra in $\mathcal{A}$ freely generated over $K$ by a set $X=\{x_{1},...,x_{n}\}$, $End A$ be the semigroup of endomorphisms of $A$, and $Aut End A$ be the group of automorphisms of the semigroup $End A$. We investigate the structure of the groups $Aut End A$ and $Aut \mathcal{A}^{\circ}$, where $\mathcal{A}^{\circ}$ is the category of finitely generated free algebras from $\mathcal{A}$. We prove that the group $Aut End A$ is generated by semi-inner and mirror automorphisms of $End F$ and the group $Aut \mathcal{A}^{\circ}$ is generated by semi-inner and mirror automorphisms of the category $\mathcal{A}^{\circ}$. This result solves an open Problem formulated in \cite{22}

Affiliated with

Also associated with

No associations

Rating

Automorphisms of the semigroup of endomorphisms of free associative algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Automorphisms of the semigroup of endomorphisms of free associative algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Automorphisms of the semigroup of endomorphisms of free associative algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-36630