Title: On the Lie algebra structure of outer derivations of finite group algebras
Speaker: Professor Markus Linckelmann, City, University of London
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Very few finite-dimensional algebras over a field are expected to arise as direct factors of finite group algebras. In fact, prominent finiteness conjectures would imply that in any fixed dimension, only finitely many isomorphism classes of algebras should arise in this way. Even in very small dimensions, where this is known to hold, this tends to require some substantial effort, since it is generally very difficult to decide for any given algebra whether it arises as a direct factor of some finite group algebra or not. Amongst many invariants which can be useful for this endeavour is the Lie algebra structure of the first Hochschild cohomology space - this is simply the space of derivations on the algebra modulo inner derivations. We describe some progress in recent years. Time permitting, we describe a construction principle for operators of degree -1 on Ext-spaces of modules which can be used to calculate the Lie algebra structure of the first Hochschild cohomology of certain finite p-group algebras. This is joint work with Radha Kessar and Dave Benson.
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