Titre du document / Document title

Strong conjugation actions induced by flags of exact Borel subalgebras

Auteur(s) / Author(s)

ZHANG Yuehui ;

Résumé / Abstract

Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u_-1eCeu.

Revue / Journal Title

Science in China. Series A. Mathematics, physics, astronomy   ISSN 1006-9283 

Source / Source

2002, vol. 45, n^o6, pp. 741-748 [8 page(s) (article)]

Langue / Language

Anglais

Editeur / Publisher

Science in China Press, Beijing, CHINE  (1996-2002) (Revue)

Localisation / Location

INIST-CNRS, Cote INIST : 7804 A1, 35400010119403.0070