Matrix wreath products of algebras and embedding theorems

2017/03/25 by Adel Alahmadi, Alahmadi, Adel, Hamed Alsulami +5
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1703.08734

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openalex publication_date 2017/03/25 · arxiv created 2017/04/03 · arxiv updated 2017/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In §\refSection6, we construct finitely generated nil algebras of arbitrary Gelfand-Kirillov dimension ≥ 8 over a countable field which answers a question from \cite8.

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