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- W2892844558 abstract "Let $k$ be an algebraically-closed field, and $B$ a unital, associative $k$-algebra with $n := dim_kB < infty$. For each $1 le m le n$, the collection of all $m$-dimensional subalgebras of $B$ carries the structure of a projective variety, which we call $operatorname{AlgGr_m(B)}$. The group $operatorname{Aut}_k(B)$ of all $k$-algebra automorphisms of $B$ acts regularly on $operatorname{AlgGr}_m(B)$. In this paper, we study the problem of explicitly describing $operatorname{AlgGr}_m(B)$, and classifying its $operatorname{Aut}_k(B)$-orbits. Inspired by recent results on maximal subalgebras of finite-dimensional algebras, we compute the homogeneous vanishing ideal of $operatorname{AlgGr}_{n-1}(B)$ when $B$ is basic, and explictly describe its irreducible components. We show that in this case, $operatorname{AlgGr}_{n-1}(B)$ is a finite union of $operatorname{Aut}_k(B)$-orbits if $B$ is monomial or its Ext quiver is Schur, but construct a class of examples to show that these conditions are not necessary." @default.
- W2892844558 created "2018-10-05" @default.
- W2892844558 creator A5037140345 @default.
- W2892844558 date "2018-09-25" @default.
- W2892844558 modified "2023-09-28" @default.
- W2892844558 title "Automorphism Groups of Finite-Dimensional Algebras Acting on Subalgebra Varieties" @default.
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