Ideals in the center of symmetric algebras

2022/07/04 by Sofia Brenner, Brenner, Sofia, Burkhard Külshammer +1
Mathematics · #16L60 (Primary) 16D25 #16N40 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2207.01281

openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study symmetric algebras A over an algebraically closed field F in which the Jacobson radical of the center of A, the socle of the center of A or the Reynolds ideal of A are ideals.

Related

• Group algebras in which the socle of the center is an ideal
• Centers associated with the Borel subalgebra of certain simple Lie\n algebras
• Classifying group algebras in which the socle of the center is an ideal
• Invariance of generalised Reynolds ideals under derived equivalences
• Central ideals and Jacobson radicals of blocks of group algebras