Journal article 1365 views
Actions of Hopf quasigroups
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...
| Published in: | Communications in Algebra |
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| Published: |
2012
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa8009 |
| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
681 |
| End Page: |
696 |