Abstract
Let RG be the group ring of a finite group G over a commutative ring R with 1. An element x in RG is said to be skew-symmetric with respect to an involution \(\sigma \) of RG if \(\sigma (x)=-x.\) A structure theorem for the Lie algebra of skew-symmetric elements of FG is given where F is an algebraic extension of \(\mathbb {Q}\) which generalizes some previously known results in this direction.
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The author was supported by DAE (Government of India) and National Board for Higher Mathematics with reference number 2/40(16)/2016/ R&D-II/5766 during this project. The author would like to thank IISER Mohali for providing good research facilities when this project was carried out. The author is very grateful to Abhay Soman for many insightful discussions. Prof. I.B.S. Passi deserves a special mention for kindling an interest of the author in the topic of the paper. Finally the author would like to thank the unknown referee whose valuable comments and suggestions helped a great deal in improving the exposition of this article.
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Chaudhuri, D. Skew-symmetric elements of rational group algebras. Beitr Algebra Geom 61, 719–729 (2020). https://doi.org/10.1007/s13366-020-00497-5
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DOI: https://doi.org/10.1007/s13366-020-00497-5