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On automorphisms of categories of free algebras of some varieties

Boris Plotkin·Grigori Zhitomirski
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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.

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Boris Plotkin, Grigori Zhitomirski. 2005-01-20. On automorphisms of categories of free algebras of some varieties. https://arxiv.org/abs/math/0501331

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