Abstract
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of the symmetric groups. We show that the first Hochschild cohomology of a positive defect block of a symmetric group is nonzero, answering in the affirmative a question of the third author. To do this, we prove a formula expressing the dimension of degree one Hochschild cohomology as a sum of dimensions of centres of blocks of smaller symmetric groups. This in turn is a consequence of a general formula that makes more precise a theorem of our previous paper describing the generating functions for the dimensions of Hochschild cohomology of symmetric groups.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
