Symmetry classes of tensors and semi-direct product of finite abelian groups |
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Authors: | Kijti Rodtes Kunlathida Chimla |
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Affiliation: | 1. Department of Mathematics, Faculty of Science, Naresuan University , Phitsanulok, Thailand.;2. Research Center for Academic Excellent in Mathematics , Phitsanulok, Thailand. |
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Abstract: | In the study of symmetry classes of tensors, finding examples of symmetry classes of tensors that possess an o*-basis is of considerable interest. There are only few classes of groups that have been provided a necessary and sufficient condition for having such a basis. There is no general criterion for any finite group yet. In this note, we provide a necessary and sufficient condition for the existence of o*-basis of symmetry classes of tensors associated with semi-direct product of some finite abelian groups and, consequently, their wreath product. |
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Keywords: | Symmetry classes of tensors o*-basis semi-direct product wreath product |
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