# Karl Hofmann (Technische Universität Darmstadt)

When:
June 23, 2020 @ 6:00 am – 8:00 am
2020-06-23T06:00:00-10:00
2020-06-23T08:00:00-10:00
Where:
Lecture held in Elysium

Title: The group algebra of a compact group and Tannaka duality for compact groups
by Karl Hofmann (Technische Universität Darmstadt) as part of Topological Groups

Lecture held in Elysium.

Abstract
In the 4th edition of the text- and handbook “The Structure of Compact Groups”,
de Gruyter, Berlin-Boston, having appeared June 8, 2020, Sidney A. Morris and
I decided to include, among material not contained in earlier editions, the Tannaka-Hochschild Duality Theorem which says that $the$ $category$ $of$ $compact$ $groups$ $is,dual$
$to$ $the$ $category,of,real,reductive$ $Hopf$ $algebras$. In the lecture I hope to explain
why this theorem was not featured in the preceding 3 editions and why we decided
to present it now. Our somewhat novel access led us into a new theory of real
and complex group algebras for compact groups which I shall discuss. Some Hopf
algebra theory appears inevitable. Recent source: K.H.Hofmann and L.Kramer,
$On$ $Weakly,Complete,Group,Algebras$ $of$ $Compact$ $Groups$, J. of Lie Theory $bold{30}$ (2020), 407-424.

Karl H. Hofmann