Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category

Jun Hu, Ngau Lam

Research output: Contribution to journalArticle

Abstract

We show that for any singular dominant integral weight λ of a complex semisimple Lie algebra g, the endomorphism algebra B of any projective-injective module of the parabolic BGG category O λ p is a symmetric algebra (as conjectured by Khovanov) extending the results of Mazorchuk and Stroppel for the regular dominant integral weight. Moreover, the endomorphism algebra B is equipped with a homogeneous (non-degenerate) symmetrizing form. In the appendix, there is a short proof due to K. Coulembier and V. Mazorchuk showing that the endomorphism algebra B λ p of the basic projective-injective module of O λ p is a symmetric algebra.

Original languageEnglish
Pages (from-to)173-201
Number of pages29
JournalJournal of Algebra
Volume515
DOIs
Publication statusPublished - 2018 Dec 1

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Injective Module
Projective Module
Endomorphism
Symmetric Algebra
Algebra
Semisimple Lie Algebra

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category. / Hu, Jun; Lam, Ngau.

In: Journal of Algebra, Vol. 515, 01.12.2018, p. 173-201.

Research output: Contribution to journalArticle

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