2017/11/23 by Alberto, Hernandez
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1711.08790
In this paper we explore the concept of depth of a ring extension when the overall algebra factorises as a product of two subalgebras, in particular the case of finite dimensional Hopf algebras. As a result we generalise the results by Kadison and Young \citeHKY on depth of a Hopf algebra H in its smash product with a finite dimensional left H-module algebra A, A#H to the context of generalised smash products Q*op#ψH \citeBz1 where Q is the quotient module coalgebra associated to the extension R⊆ H of finite dimensional Hopf algebras \citeKa2\citeHKY\citeH. Moreover, following the construction of double crossed products in \citeMa and \citeMa1 we use our result on factorisation algebras to get a general result on the depth of the extension of a Hopf algebra H in its Drinfel\vtick d double D(H). Keywords : Depth, Factorisation Algebra, Smash Product, Drinfel\vtick d Double, Double Crossed Product, Normal Extension. Subject classification: 20C05, 20G05, 16W30, 17B37, 13E10.