Open Access
2013 Conjugacy classes of left ideals of a finite dimensional algebra
Arkadiusz Mȩcel, Jan Okniński
Publ. Mat. 57(2): 477-496 (2013).


Let $A$ be a finite dimensional unital algebra over a field $K$ and let $C(A)$ denote the set of conjugacy classes of left ideals in $A$. It is shown that $C(A)$ is finite if and only if the number of conjugacy classes of nilpotent left ideals in $A$ is finite. The set~$C(A)$ can be considered as a semigroup under the natural operation induced from the multiplication in $A$. If $K$ is algebraically closed, the square of the radical of~$A$ is zero and $C(A)$ is finite, then for every $K$-algebra $B$ such that $C(B)\cong C(A)$ it is shown that $B\cong A$.


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Arkadiusz Mȩcel. Jan Okniński. "Conjugacy classes of left ideals of a finite dimensional algebra." Publ. Mat. 57 (2) 477 - 496, 2013.


Published: 2013
First available in Project Euclid: 12 December 2013

zbMATH: 1292.16013
MathSciNet: MR3114779

Primary: 16D99 , 16P10 , 20M99

Keywords: conjugacy class , Finite dimensional algebra , left ideal , semigroup

Rights: Copyright © 2013 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.57 • No. 2 • 2013
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