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Some problems concerning quasi-hereditary algebras

Some problems concerning quasi-hereditary algebras
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Quasi-Hereditary Extension Algebras

Algebras and Representation Theory, 2003
Quasi-hereditary algebras \(A\) have finite global dimension. Thus their `homological dual', that is, the Yoneda extension algebra of the sum \(L\) of simple modules, \(B=\text{Ext}^*_A(L,L)\), again is a finite dimensional algebra. In some of the most prominent classes of quasi-hereditary algebras, such as Schur algebras or blocks of category ...
Ágoston, István, Dlab, Vlastimil, Lukács, Erzsébet   +2 more
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Quasi-Hereditary Endomorphism Algebras

Canadian Mathematical Bulletin, 1995
AbstractQuasi-hereditary algebras were introduced by Cline-Parshall-Scott (see [CPS] or [PS]) to deal with highest weight categories which occur in the study of semi-simple complex Lie algebras and algebraic groups. In fact, the quasi-hereditary algebras which appear in these applications enjoy a number of additional properties.
Dlab, V., Heath, P., Marko, F.
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Quasi-hereditary slim cyclotomic q-Schur algebras

Journal of Pure and Applied Algebra, 2023
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Deng, Bangming, Yang, Guiyu
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Δ-tame quasi-hereditary algebras

Science in China Series A: Mathematics, 2007
Let (K, M, H) be an upper triangular biomodule problem. Brustle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K, M, H) is quasi-hereditary, and there is an equivalence between the category of Δ-good modules of A and Mat(K, M). In this note, based on the tame theorem for
Yun-ge Xu, Ying-bo Zhang
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Triangular matrix algebras over affine quasi-hereditary algebras

Linear Algebra and its Applications, 2022
Quasi-hereditary algebras (and its module categories called highest weight categories) were introduced by \textit{E. Cline} et al. [J. Reine Angew. Math. 391, 85--99 (1988; Zbl 0657.18005)] with many applications to representation theory and other related fields. There are many ways to construct new quasi-hereditary algebras from old ones. Affine quasi-
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Quasi-hereditary algebras related to local algebras

Communications in Algebra, 1998
For ⋀ a finite dimensional local algebra with radical N where Nn = 0 ≠ N n-1 define (as a right A-module), then A(⋀) is quasi-hereditary and it has a unique heredity ideal J 1(A).Assume ⋀ satisfies the right socle condition (the socle series and the radical series of ⋀⋀ coincide). We show that then the algebra Ai/J1 (Ai-1 ) is isomorphic to A i-1 where
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Semilocal modules and quasi-hereditary algebras

Archiv der Mathematik, 1993
Let \(A\) be a finite-dimensional algebra over an algebraically closed field \(k\) and \(N\) the Jacobson radical of \(A\). If \(M\) is a finitely generated semilocal \(A\)-module with Loewy length \(m\), then \(\text{End}_ A(\bigoplus^ m_{i=1}M/N^ iM)\) is a quasi-hereditary algebra.
YANAN LIN, CHANGCHANG XI
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Ringel duals of quasi-hereditary algebras

Communications in Algebra, 1996
(1996). Ringel duals of quasi-hereditary algebras. Communications in Algebra: Vol. 24, No. 9, pp. 2825-2838.
Bangming Deng, Changchang Xi
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A construction of quasi-hereditary endomorphism algebras

Applied Mathematics-A Journal of Chinese Universities, 2014
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