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The duality theorem for twisted smash products of Hopf algebras and its applications

Volume 141 / 2015

Zhongwei Wang, Liangyun Zhang Colloquium Mathematicum 141 (2015), 25-44 MSC: Primary 16T05, 16S30. DOI: 10.4064/cm141-1-3

Abstract

Let $A\mathbin {\#_T}H$ denote the twisted smash product of an arbitrary algebra $A$ and a Hopf algebra $H$ over a field. We present an analogue of the celebrated Blattner–Montgomery duality theorem for $A\mathbin {\#_T}H$, and as an application we establish the relationship between the homological dimensions of $A\mathbin {\#_T}H$ and $A$ if $H$ and its dual $H^*$ are both semisimple.

Authors

  • Zhongwei WangDepartment of Basic Science
    Jinling Institute of Technology
    Nanjing 210069, P.R. China
  • Liangyun ZhangCollege of Science
    Nanjing Agricultural University
    Nanjing 210095, P.R. China
    e-mail

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