Actions of Hopf quasigroups
Tomasz Brzezi\'nski, Zhengming Jiao
TL;DR
This paper explores actions of Hopf quasigroups, defining Long dimodules, constructing solutions to Militaru's D-equation, and establishing compatibility conditions for smash product constructions.
Contribution
It introduces the concept of Long dimodules for Hopf quasigroups and provides new solutions to Militaru's D-equation, advancing the understanding of their actions and smash products.
Findings
Defined Long dimodules for Hopf quasigroups and coquasigroups
Constructed solutions to Militaru's D-equation
Derived compatibility conditions for smash product construction
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 D-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.
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Taxonomy
Topicsgraph theory and CDMA systems · Mathematics and Applications · Advanced Combinatorial Mathematics