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SUMMARY:Teresa Conde (University Of Stuttgart)
DTSTART:20210106T150000Z
DTEND:20210106T160000Z
DTSTAMP:20260423T024537Z
UID:TRAC/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TRAC/1/">Qua
 sihereditary algebras with exact Borel subalgebras</a>\nby Teresa Conde (U
 niversity Of Stuttgart) as part of The TRAC Seminar - Théorie de Représe
 ntations et ses Applications et Connections\n\n\nAbstract\nExact Borel sub
 algebras of quasihereditary algebras emulate the role of "classic" Borel s
 ubalgebras of complex semisimple Lie algebras. Not every quasihereditary a
 lgebra A has an exact Borel subalgebra. However\, a theorem by Koenig\, K
 ülshammer and Ovsienko establishes that there always exists a quasiheredi
 tary algebra Morita equivalent to A that has a (regular) exact Borel subal
 gebra. Despite that\, an explicit characterisation of such "special" Morit
 a representatives is not directly obtainable from Koenig\, Külshammer and
  Ovsienko's work. In this talk\, I shall present a numerical criterion to 
 decide whether a quasihereditary algebra contains a regular exact Borel su
 balgebra and I will provide a method to compute all Morita representatives
  of A that have a regular exact Borel subalgebra. We shall also see that t
 he Cartan matrix of a regular exact Borel subalgebra of a quasihereditary 
 algebra A only depends on the composition factors of the standard and cost
 andard A-modules and on the dimension of the Hom-spaces between standard A
 -modules. I will conclude the talk with a characterisation of the basic qu
 asihereditary algebras that admit a regular exact Borel subalgebra.\n
LOCATION:https://researchseminars.org/talk/TRAC/1/
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