Hebrew University 
 
Amitsur Algebra Seminar
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Time: Thursday, Nov 29 , 12:00-13:15
 
Place: math 209
 
Speaker: Uriya First (HUJI)
 
Title: Solution to The Isomorphism Problem of Systems of Bilinear
Forms Over Certain Rings
 
Abstract:
The isomorphism problem of nondegenerate (non-symmetric) bilinear
forms of fields was solved by Carl Riehm in 1974, where solution means
reduction to the isomorphism problem of hermitian forms. This solution
was extended to degenerate forms by Gabriel, to sesqulinear forms by
Riehm and Shrader-Frechette and to systems of two forms by Sergeichuk
and others.
 
In my talk I will present a new notion of bilinear forms over
(non-commutative) rings (no involution on the base ring is needed) and
then present a solution to the isomorphism problem of arbitrarily
large systems of bilinear forms over "good" rings. Here "good" means
artinian (and more generally, pro-semiprimary semiperfect, e.g. f.d.
algebras over the p-adic integers) and "solution" means reduction to
(1) isomorphism of hermitian forms and (2) isomorphism of objects in a
certain abelian category.
 
The methods involved have many applications including:
- Witt's reduction theorem (over rings; for systems of bilinear forms)
- Every bilinear form admits a unique representation as a sum of isotypes.
- Classification of all indecomposable bilinear spaces.
More applications will be presented if time permits.
 
The lecture will also include a survey of Riehm's original solution.
 
You are cordially invited!
 
 <http://math.huji.ac.il/amitsur.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>