Skew-Symmetric Elements of Rational Group Algebras

Dishari Chaudhuri

Skew-Symmetric Elements of Rational Group Algebras

Rings and Algebras 2020-03-24 v5

Authors: Dishari Chaudhuri

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 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.

Keywords

group ring skew-symmetric elements involution structure theorem algebraic extension

Cite

@article{arxiv.1805.01218,
  title  = {Skew-Symmetric Elements of Rational Group Algebras},
  author = {Dishari Chaudhuri},
  journal= {arXiv preprint arXiv:1805.01218},
  year   = {2020}
}

Comments

Main result generalized from $\mathbb{Q}G$ to $FG$ where $F$ is an algebraic extension of $\mathbb{Q}$. Major changes in the exposition done. 12 pages

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