Computation of A∞ algebras in group cohomology
The applicability of A1-structures, as introduced by Stasheff (1963) in the setting of algebra, or more specifically in representation theory has gradually grown. With Keller (2002, 2001) and Lu, Palmieri, Wu, and Zhang (2007, 2006), the benefits of A1-algebra structures to the theory of representations and of cohomology of various classes of algebras have been made explicit. By the results in these papers, there is the potential to use A1-structures in modular group cohomology – the group cohomology A1-algebra would determine the corresponding group ring completely. However, the calculational techniques available do not lend themselves easily to calculation of these structures, nor are there particularly many examples at hand. The only examples that do exist in deeper treatment for modular finite group cohomology are the finite cyclic groups.