Orthogonal bases of brauer symmetry classes of tensors for groups having cyclic support on nonlinear brauer characters

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Electronic Journal of Linear Algebra, ISSN: 1081-3810, Vol: 31, Issue: 1, Page: 263-285

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http://repository.uwyo.edu/ela/vol31/iss1/20; http://publications.lib.chalmers.se/publication/238975
Hormozi, Mahdi; Rodtes, Kijti
University of Wyoming Libraries
Mathematics; Brauer symmetry classes of tensors; Orthogonal basis; Semi-dihedral groups; Dicyclic groups; Algebra
article description
This paper provides some properties of Brauer symmetry classes of tensors. A dimension formula is derived for the orbital subspaces in the Brauer symmetry classes of tensors corresponding to the irreducible Brauer characters of the groups whose non-linear Brauer characters have support being a cyclic group. Using the derived formula, necessary and sufficient condition are investigated for the existence of an o-basis of dicyclic groups, semi-dihedral groups, and also those things are reinvestigated on dihedral groups. Some criteria for the non-vanishing elements in the Brauer symmetry classes of tensors associated to those groups are also included.