Abstract
If we have a braid group acting on a derived category by spherical twists, how does a lift of the longest element of the symmetric group act? We give an answer to this question, using periodic twists, for the derived category of modules over a symmetric algebra. The question has already been answered by Rouquier and Zimmermann in a special case. We prove a lifting theorem for periodic twists, which allows us to apply their answer to the general case.
Along the way we study tensor products in derived categories of bimodules. We also use the lifting theorem to give new proofs of two known results: the existence of braid relations and, using the theory of almost Koszul duality due to Brenner, Butler, and King, the result of Rouquier and Zimmermann mentioned above.
Along the way we study tensor products in derived categories of bimodules. We also use the lifting theorem to give new proofs of two known results: the existence of braid relations and, using the theory of almost Koszul duality due to Brenner, Butler, and King, the result of Rouquier and Zimmermann mentioned above.
Original language  English 

Pages (fromto)  16311669 
Number of pages  9 
Journal  Transactions of the American Mathematical Society 
Volume  367 
Issue number  3 
Early online date  5 Sep 2014 
DOIs  
Publication status  Published  2015 
Profiles

Joseph Grant
 School of Engineering, Mathematics and Physics  Lecturer in Pure Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research