On automorphisms of categories of free algebras of some varieties

Abstract

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the variety of all free associative K-algebras over an infinite field K and 2) for the variety of all representations of groups in unital R-modules over a commutative associative ring R with unit. It turns out that they are almost inner in a sense.

32 pages. Continuation of math.CT/0411408, 2004

References in corpus (3)

• Algebras with the same (algebraic) geometry
• Seven Lectures on the Universal Algebraic Geometry
• The group of automorphisms of the category of free associative algebras

Cited by in corpus (6)

• Automorphisms of the endomorphism semigroup of a free commutative algebra
• Automorphic equivalence of the representations of Lie algebras
• Automorphisms of the semigroup of all endomorphisms of free algebras
• Automorphisms of the semigroup of endomorphisms of free algebras of homogeneous varieties
• Aupomorphisms of the category of the free nilpotent groups of the fixed class of nilpotency
• On automorphisms of categories