Automorphisms of categories of free algebras of some varieties

[摘要] Let V be a variety of universal algebras. We suggest a method for describing automorphisms of the category of free V-algebras. All automorphisms of such categories are found in two cases: (1) V is the variety of all associative K-algebras over an infinite field K; (2) V is the variety of all representations of groups in unital R-modules over a commutative associative ring R with unit. We prove that all these automorphisms are close to inner automorphisms. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] automorphisms of categories;inner automorphisms;free algebras;associative algebras;group representations;universal algebraic geometry