Dear Colleagues and Students,
You are cordially invited to the Algebra Seminar organized by the Department of Mathematics.
Speaker: Matthew Gelvin (Bilkent)
“Unital biinvariant bases in source algebras of blocks”
Abstract: Every finite dimensional algebra over an infinite field has a basis consisting of units. If the algebra is interior for a finite p-group D, we say that it is a bipermutation D-algebra if there is a basis that is invariant under left and right D-multiplication. Such a basis may be viewed as a (D,D)-biset, and if the basis can be chosen to consist of units, it (almost) determines a saturated fusion system on D.
This talk, based on joint work with Laurence Barker, will have two goals: To explain the material in the above paragraph in greater detail, and to show how certain structural properties of an algebra are equivalent to the existence of a unital biinvariant basis. The ultimate goal–applying these results to the source algebra of a block–will be outlined at the end, time permitting.
Date: October 16, 2019
Place: SA – 141