Endomorphism Algebras of F(Δ) over Quasi-hereditary Algebras

✍ Scribed by C.C Xi

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 592 KB
• Volume: 175
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1995.1221

✦ Synopsis

Let (A) be a finite-dimensional algebra over an algebraically closed field. If (A) is an (\mathscr{F}(\Delta))-finite quasi-hereditary algebra, then the endomorphism algebra of the direct sum of all non-isomorphic indecomposable (\Delta)-good modules over (A) is quasi-hereditary. Moreover, this endomorphism algebra is left QF-3 if and only if the injective direct summand of the characteristic module (T) cogenerates (T).
c) 1995 Academic Press, Inc.