EPSRC Reference: 
EP/M02525X/1 
Title: 
Integrable derivations and Hochschild cohomology of block algebras of finite groups 
Principal Investigator: 
Linckelmann, Professor M 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Sch of Engineering and Mathematical Sci 
Organisation: 
City, University of London 
Scheme: 
Standard Research 
Starts: 
01 April 2015 
Ends: 
31 August 2018 
Value (£): 
341,698

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
03 Mar 2015

EPSRC Mathematics Prioritisation Panel March 2015

Announced


Summary on Grant Application Form 
The product rule of the all familiar operation of taking derivatives of real valued functions has a plethora
of generalisations and applications in algebra. It leads to the notion of derivations of algebras  these
are linear endomorphisms of an algebra satifying the product rule. They represent the classes of
the first Hochschild cohomology of an algebra. The first Hochschild cohomology of an algebra
turns out to be a Lie algebra, and more precisely, a restricted Lie algebra if the underlying
base ring is a field of positive characteristic. The (restricted) Lie algebra structure extends to
all positive degrees in Hochschild cohomology  this goes back to pioneering work of Gerstenhaber
on defornations of algebras.
Modular representation theory of finite groups seeks to understand the connections between
the structure of finite groups and the associated group algebras. Many of the conjectures that drive
this area are  to date mysterious  numerical coincidences relating invariants of finite
group algebras to invariants of the underlying groups. The sophisticated cohomological
technology hinted at in the previous paragraph is expected to yield some insight regarding these
coincidences, and the present proposal puts the focus on some precise and unexplored
invariance properties of certain groups of integrable derivations under Morita, derived, or stable
equivalences between indecomposable algebra factors of finite group algebras, their character theory,
their automorphism groups, and the local structure of finite groups.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

Organisation Website: 
http://www.city.ac.uk 