On the Teichmüller map and a class of nonassociative algebras

Seminar
Speaker
Prof. Darrell Haile (Indiana University)
Date
25/03/2015 - 12:15 - 11:15Add to Calendar 2015-03-25 11:15:00 2015-03-25 12:15:00 On the Teichmüller map and a class of nonassociative algebras This is joint work with Yuval Ginosar.  Let K/F be a finite Galois extension with Galois group G.  The Teichmüller map is a function that associates to every central simple K-algebra B normal over F an element of H^3(G, K*).  The value of the function is trivial precisely when the class of B is restricted from F.  The classical definition of this map involves the use of a crossed-product algebra over B.  The associativity of this algebra is also equivalent to the class of B being restricted from F.  The aim of this lecture is to elucidate the nature of the nonassociative algebras that arise when B is normal but not restricted.  It turns out that the resulting theory is remarkably similar to the theory of associative algebras arising from the noninvertible cohomology of a Galois extension L/F such that L contains K, and I want to explain that relationship. Third floor seminar room אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room
Abstract

This is joint work with Yuval Ginosar.  Let K/F be a finite Galois extension with Galois group G.  The Teichmüller map is a function that associates to every central simple K-algebra B normal over F an element of H^3(G, K*).  The value of the function is trivial precisely when the class of B is restricted from F.  The classical definition of this map involves the use of a crossed-product algebra over B.  The associativity of this algebra is also equivalent to the class of B being restricted from F.  The aim of this lecture is to elucidate the nature of the nonassociative algebras that arise when B is normal but not restricted.  It turns out that the resulting theory is remarkably similar to the theory of associative algebras arising from the noninvertible cohomology of a Galois extension L/F such that L contains K, and I want to explain that relationship.

תאריך עדכון אחרון : 16/03/2015