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Exact Borel subalgebras of path algebras of quivers of Dynkin type A

JOURNAL OF PURE AND APPLIED ALGEBRA (2024)

Combinatorics of quasi-hereditary structures

Manuel Flores et al.

Summary: The article investigates quasi-hereditary algebras and structures on given algebras, providing a full classification for path algebras of Dynkin type A and a counting method for types D and E. Necessary and sufficient conditions for posets of quasi-hereditary structures to be lattices are also presented.

JOURNAL OF COMBINATORIAL THEORY SERIES A (2022)

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The Ext-algebra of standard modules over dual extension algebras

Markus Thuresson

Summary: We explore the isomorphism of associative algebras between the Ext-algebras of standard modules over the dual extension algebras of two directed algebras B and A, and describe the A(infinity)-structures on these Ext-algebras under certain technical assumptions.

JOURNAL OF ALGEBRA (2022)

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All quasihereditary algebras with aregular exact Borel subalgebra

Teresa Conde

Summary: This paper provides a criterion to determine whether a quasihereditary algebra contains a regular exact Borel subalgebra and presents a method to compute all representatives of A that have a regular exact Borel subalgebra. It is also shown that the Cartan matrix of a regular exact Borel subalgebra depends only on the composition factors of standard and costandard A-modules and the dimension of the Hom-spaces between standard A-modules. Additionally, the paper characterises the basic quasihereditary algebras that admit a regular exact Borel subalgebra.

ADVANCES IN MATHEMATICS (2021)

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