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<p>This article studies the compatibility of Koenig’s notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide bounds for the multiplicities of indecomposable projectives in the principal blocks of BGG category <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {O}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">O</mi> </math></EquationSource> </InlineEquation> having basic regular exact Borel subalgebras.</p>

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Exact Borel subalgebras, idempotent quotients and idempotent subalgebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月9日

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  • Teresa Conde,
  • Julian Külshammer

摘要

This article studies the compatibility of Koenig’s notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide bounds for the multiplicities of indecomposable projectives in the principal blocks of BGG category \(\mathcal {O}\) O having basic regular exact Borel subalgebras.