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! <http://math.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Konstantin Golubev <kgolubev@gmail.com>