nLab Takeuchi product

Given an associative algebra AA, with enveloping algebra A e=AA opA^e = A\otimes A^{op}, the Takeuchi product × A\times_A is certain product in the category of AA-rings. It generalizes a construction of M. E. Sweedler where AA is commutative; Sweedler’s article may be itself viewed in a sense a “generalization of the relative Brauer group and the associated theory”.

Takeuchi product is used in the theory of associative bialgebroids over noncommutative base.

  • Mitsuhiro Takeuchi, Groups of algebras over A×A¯A \times \bar{A}, J. Math. Soc. Japan 29, 459–492, 1977, MR0506407, euclid
  • M. E. Sweedler, Groups of simple algebras, Publ. IHES 44, 79–189, MR51:587, numdam
  • T. Brzeziński, G. Militaru, Bialgebroids, × R\times_{R}-bialgebras and duality, J. Algebra 251: 279-294, 2002, math.QA/0012164
  • P. Schauenburg, Bialgebras over noncommutative rings and a structure theorem for Hopf bimodules, Appl. Categ. Structures 6 (1998), 193–222, ps doi
category: algebra

Last revised on October 2, 2014 at 12:43:10. See the history of this page for a list of all contributions to it.