Photo by vika_strawberrika from unsplash
Abstract In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite… Click to show full abstract
Abstract In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite gyrogroup on a finite-dimensional complex inner product space is unitary and hence is completely reducible using strong connections between linear actions of groups and gyrogroups. Also, we provide an example of a unitary representation of an arbitrary finite gyrogroup, which resembles the group-theoretic left regular representation.
Keywords:
complete reducibility;
gyrogroup;
gyrogroup representations;
finite gyrogroup;
reducibility gyrogroup;
representation
Journal Title: Communications in Algebra
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Communications in Algebra
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!