Conjugacy classes of left ideals of a finite dimensional algebra
Meçel, Arkadiusz (Warsaw University (Polònia). Institute of Mathematics)
Okniński, Jan (Warsaw University (Polònia). Institute of Mathematics)

Date:	2013
Abstract:	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) ≡ C(A) it is shown that B ≡ A.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Finite dimensional algebra ; Left ideal ; Semigroup ; Conjugacy class
Published in:	Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 477-496, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287161
DOI: 10.5565/PUBLMAT_57213_10

20 p, 366.0 KB

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