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Automorphisms of categories of free algebras of varieties

Authors: G. Mashevitzky, B. Plotkin and E. Plotkin
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 1-10
MSC (2000): Primary 08A35, 08CO5, 14A22, 14A99
Published electronically: March 13, 2002
MathSciNet review: 1911740
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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 $\Theta$.

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Additional Information

G. Mashevitzky
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, 84105, Israel

B. Plotkin
Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem, 91904, Israel

E. Plotkin
Affiliation: Department of Mathematics, Bar Ilan University, Ramat Gan, 52900, Israel

Keywords: Algebraic variety, variety of algebras, category, free algebra, automorphisms
Received by editor(s): July 4, 2001
Published electronically: March 13, 2002
Additional Notes: 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”.
Communicated by: Efim Zelmanov
Article copyright: © Copyright 2002 American Mathematical Society