2025/07/03 by Han, Xiao, Majid, Shahn · 1 citation
#16T05 #20G42 #46L87 #58B32 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2507.02848
We introduce a cotwist construction for Hopf algebroids that also entails cotwisting or `quantisation' of the base and which is dual to a previous twisting construction of P. Xu. Whereas the latter applied the construction to the algebra of differential operators on a classical base B, we show that the dual of this is the algebra of sections J(B) of the jet bundle and hence that the latter forms a Hopf algebroid. This is constructed for commutative algebras B in a pro-object setting via quotients of the pair Hopf algebroid B⊗ B and can then be deformed by our cotwist construction to give a possibly noncommutative jet Hopf algebroid over a noncommutative base. We also observe in the commutative case that Jk(B) for jets of order k can be identified with J1(Bk) where Bk denotes B equipped with a certain noncommutative first order differential calculus.