Hebrew University 
Amitsur Algebra Seminar
Time: Thursday, Apr 18, 12:00-13:15
Place: math 209
Title: Automorphic equivalence of the many-sorted algebras
Speaker: Arkady Tsurkov (Bar Ilan) 
Abstract: Universal algebras $H_{1}$, $H_{2}$ of the variety
$\Theta $ are geometrically equivalent if they have same
structure of the algebraic closed sets. Automorphic
equivalence of algebras is a generalization of this notion. We
can say that universal algebras $H_{1}$, $H_{2}$ of the
variety $% \Theta $ are geometrically equivalent if the
structures of the structures of the algebraic closed sets of
these algebras coincides up to changing of coordinates defined
by some automorphism of the category $\Theta ^{0}$. $% \Theta
^{0}$ is a category of the free finitely generated algebras of
the variety $\Theta $. The quotient group $\mathfrak{A/Y}$
determines the difference between geometric and automorphic
equivalence of algebras of the variety $\Theta $, where
$\mathfrak{A}$ is a group of the all automorphisms of the
category $\Theta ^{0}$, $\mathfrak{Y}$ is a group of the all
inner automorphisms of this category. The method of the verbal
operations was worked out in: B. Plotkin, G. Zhitomirski,
\textit{On automorphisms of categories of free algebras of
some varieties}, 2006 - for the calculation of the group
$\mathfrak{A/Y}$. By this method the automorphic equivalence
was reduced to the geometric equivalence in: A. Tsurkov,
\textit{Automorphic equivalence of algebras}, 2007. All these
results were true for the one-sorted algebras: groups,
semigroups, linear algebras... Now we reprove these results
for the many-sorted algebras: representations of groups,
actions of semigroups over sets and so one. 
You are cordially invited!
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Konstantin Golubev   <kgolubev@gmail.com>