Matrix wreath products of algebras and embedding theorems

Alahmadi, Adel; Alsulami, Hamed; Jain, S.; Zelmanov, Efim

doi:10.1090/tran/7642

Matrix wreath products of algebras and embedding theorems
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by Adel Alahmadi, Hamed Alsulami, S. K. Jain and Efim Zelmanov PDF

Trans. Amer. Math. Soc. 372 (2019), 2389-2406 Request permission

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 §6, we construct finitely generated nil algebras of arbitrary Gelfand-Kirillov dimension $\geq 8$ over a countable field which answers a question from [New trends in noncommutative algebra, Amer. Math. Soc., Providence, RI, 2012, pp. 41–52].

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