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Actions of Hopf quasigroups / Tomasz Brzezinski

Communications in Algebra, Volume: 40, Issue: 2, Pages: 681 - 696

Swansea University Author: Tomasz, Brzezinski

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DOI (Published version): 10.1080/00927872.2010.535588

Abstract

Definitions of actions of Hopf quasigroups are discussed in the context of Long dimodules and smash products. In particular, Long dimodules are defined for Hopf quasigroups and coquasigroups, and solutions to Militaru's -equation are constructed. A necessary compatibility condition between acti...

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Published in: Communications in Algebra
Published: 2012
URI: https://cronfa.swan.ac.uk/Record/cronfa8009
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Abstract: Definitions of actions of Hopf quasigroups are discussed in the context of Long dimodules and smash products. In particular, Long dimodules are defined for Hopf quasigroups and coquasigroups, and solutions to Militaru's -equation are constructed. A necessary compatibility condition between action and multiplication of a Hopf quasigroup acting on its quasimodule Hopf quasigroup for a smash product construction is derived. This necessary condition takes the form of the associativity of the action up to an antipodal operation. In the case of a Hopf quasigroup with a bijective antipode it is simply the associativity of the action, a condition assumed a priori by Klim and Majid in their original construction of smash products of Hopf quasigroups.
College: College of Science
Issue: 2
Start Page: 681
End Page: 696