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Jordan homomorphisms: A survey
Matej Brešar, Efim Zelmanov
The paper surveys the history and state-of-the-art of the study of Jordan homomorphisms.
Jordan homomorphisms and T-ideals
Matej Brešar, Efim Zelmanov
Let and be associative algebras over a field with {\rm char}. Our first main result states that if is unital and equal to its commutator ideal, then every…
Simple Jordan superalgebras with the even parts of Clifford type
Ivan Shestakov, Efim Zelmanov
The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensiona…
On Lie isomorphisms of rings
Oksana Bezushchak, Iryna Kashuba, Efim Zelmanov
An associative ring gives rise to the Lie ring . The subject of isomorphisms of Lie rings and has attracted considerable attention i…
Cyclic homology of Jordan superalgebras and related Lie superalgebras
Consuelo Martínez, Efim Zelmanov, Zezhou Zhang
We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan…
Automorphisms and derivations of affine commutative and PI-algebras
Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov
We prove analogs of A.~Selberg's result for finitely generated subgroups of and of Engel's theorem for subalgebras of for a finitely generated assoc…
Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth
Be'eri Greenfeld, Efim Zelmanov
We construct finitely generated nil algebras with prescribed growth rate. In particular, any increasing submultiplicative function is realized as the growth function of a nil algeb…