Tuesday, September 12, 2023 4pm to 5pm
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24 Race Street, Athens, Ohio 45701
Algebra Seminar | Symmetry Questions about Amenability and simplicity of Bases, Sept. 12
The Algebra Seminar series presents Fatma Ebrahim, of Al-Azhar University from Cairo, Egypt, discussing "Symmetry Questions about Amenability and simplicity of Bases" on Tuesday, Sept. 12, from 4-5 p.m. in Morton 222.
Abstract: The study of notions of amenability, congeniality and simplicity of bases for infinite dimensional algebras is furthered. A basis $\mathcal{B}$ over an infinite dimensional $F$-algebra $\mathcal{A}$ is called amenable if $F^{\mathcal{B}$, the direct product indexed by $\mathcal{B}$ of copies of the field $F$, can be made into an $\mathcal{A}$-module in a natural way. An amenable basis $\mathcal{B}$ is called simple if it is not properly congenial to any other amenable basis. Graph magma algebras are a suitable non-commutative setting for these considerations. In this talk, we focus on characterizing left and right amenability and simplicity of the so-called bases of vertices (or permissible bases) of such algebras. It is shown, among other results, that finite support magma algebras have no simple left or right bases.
[This talk reports on ongoing collaborative research with S. Lopez-Permouth and M. Zailaee.]
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