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Automorphisms of categories of free algebras of varieties
Author(s):
G.
Mashevitzky;
B.
Plotkin;
E.
Plotkin
Journal:
Electron. Res. Announc. Amer. Math. Soc.
8
(2002),
1-10.
MSC (2000):
Primary 08A35, 08CO5, 14A22, 14A99
Posted:
March 13, 2002
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Abstract:
Let  be an arbitrary variety of algebras and let  be the category of all free finitely generated algebras from  . We study automorphisms of such categories for special  . 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  .
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Additional Information:
G.
Mashevitzky
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, 84105, Israel
Email:
gmash@cs.bgu.ac.il
B.
Plotkin
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, 91904, Israel
Email:
borisov@math.huji.ac.il
E.
Plotkin
Affiliation:
Department of Mathematics, Bar Ilan University, Ramat Gan, 52900, Israel
Email:
plotkin@macs.biu.ac.il
DOI:
10.1090/S1079-6762-02-00099-9
PII:
S 1079-6762(02)00099-9
Keywords:
Algebraic variety,
variety of algebras,
category,
free algebra,
automorphisms
Received by editor(s):
July 4, 2001
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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