Geometrical Equivalence and Action Type Geometrical Equivalence of Group Representations

TL;DR

This paper demonstrates that action-type geometrical equivalence and group geometrical equivalence do not necessarily imply overall geometrical equivalence of group representations, highlighting limitations in current equivalence criteria.

Contribution

It provides a counterexample showing the non-implication between different types of geometrical equivalences in group representations.

Findings

Counterexample disproves the implication from action-type to overall geometrical equivalence.

Highlights the independence of different geometrical equivalence notions in group representations.

Clarifies limitations in the criteria for classifying group representations based on geometrical equivalence.

Abstract

In this paper we present the example which proves that we can not conclude the geometrical equivalence of group representations from the corresponding action-type geometrical equivalence and group geometrical equivalence.