Automorphisms of the semigroup of all endomorphisms of free algebras

Abstract

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups, modules, Lie algebras and some others. All these researches were inspired by the questions prof. B. Plotkin set in connection with so called universal algebraic geometry (see for example Arxiv:math, GM/0204245). The aim of this paper is to suggest a method of describing the group AutEnd(F) for a free finitely generated algebra F of an arbitrary variety of universal algebras. This method allows to obtain easily all known results as well as new ones.

17 pages

References in corpus (5)

• Algebras with the same (algebraic) geometry
• Seven Lectures on the Universal Algebraic Geometry
• Automorphisms of categories of free modules and free Lie algebras
• The group of automorphisms of the category of free associative algebras
• On automorphisms of categories of free algebras of some varieties

Cited by in corpus (4)

• Automorphisms of the endomorphism semigroup of a free commutative algebra
• Automorphisms of the semigroup of endomorphisms of free algebras of homogeneous varieties
• The Largest Subsemilattices of the Endomorphism Monoid of an Independence Algebra
• Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry