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Automorphisms of categories of free algebras of varieties
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## Automorphisms of categories of free algebras of varieties

### G. Mashevitzky, B. Plotkin, and E. Plotkin

**Abstract.**
Let $\Theta$ be an arbitrary variety of algebras
and let $\Theta^0$ be the category of all free
finitely generated algebras from $\Theta$. We study
automorphisms of such categories for special
$\Theta$. The cases of the varieties of all groups,
all semigroups, all modules over a noetherian ring,
all associative and commutative algebras over a field
are completely investigated. The cases of associative and Lie algebras
are also considered. This topic relates to algebraic geometry
in arbitrary variety of algebras $\Theta$.

*Copyright 2002 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**08** (2002), pp. 1-10
- Publisher Identifier: S 1079-6762(02)00099-9
- 2000
*Mathematics Subject Classification*. Primary 08A35, 08CO5, 14A22, 14A99
*Key words and phrases*. Algebraic variety, variety of algebras, category, free algebra, automorphisms
- Received by the editors July 4, 2001
- Posted on March 13, 2002
- Communicated by Efim Zelmanov
- Comments (When Available)

**G. Mashevitzky**

Department of Mathematics, Ben Gurion University of the Negev, 84105, Israel

*E-mail address:* `gmash@cs.bgu.ac.il`

**B. Plotkin**

Institute of Mathematics, The Hebrew University, Jerusalem, 91904, Israel

*E-mail address:* `borisov@math.huji.ac.il`

**E. Plotkin**

Department of Mathematics, Bar Ilan University, Ramat Gan, 52900, Israel

*E-mail address:* `plotkin@macs.biu.ac.il`

This work was supported in part by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities -- Center of Excellence Program and by Intas grant ``Algebraic $K$-theory, groups and algebraic homotopy theory''.

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