Markus Linckelmann

City, University of London


Generating functions for the Hochschild cohomology of symmetric groups


Algebra Seminar


1st March 2023, 2:30 pm – 3:30 pm
Fry Building, 2.04


We start out by reviewing some classical material on the representation
theory of symmetric groups and the Hochschild cohomology of
finite-dimensional algebras. We describe generating functions for the
dimensions of the Hochschild cohomology of symmetric groups in each degree.
While it is known, using the classification of finite simple groups, that
the first Hochschild cohomology of a non-semisimple finite group algebra is
non-zero, it remains an open question whether this is true for non-simple
blocks of finite groups. We use generating functions to show that the first
Hochschild cohomology of any non-simple block of a symmetric group algebra
is non-zero. This is joint work with Dave Benson and Radha Kessar.





Organisers: James Maxwell, Vlad Vankov

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