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Oriented group involutions in group algebras: a survey

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Abstract

Let \(\circledast :{\mathbb {F}}G\rightarrow {\mathbb {F}}G\) denote the involution obtained as a linear extension of an involution of G, twisted by the homomorphism \(\sigma :G\rightarrow \{\pm 1\}\). In this survey we gather some results concerning to the Lie properties of symmetric and skew-symmetric elements and the corresponding group identities satisfied by the set of symmetric units, and when these identities determine the structure of the whole group algebra \({\mathbb {F}}G\) [resp. unit group \({\mathcal {U}}({\mathbb {F}}G)\)].

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Correspondence to John H. Castillo.

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Dedicated to Professor César Polcino Milies on the occasion of his 70th birthday.

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Castillo, J.H., Holguín-Villa, A. Oriented group involutions in group algebras: a survey. São Paulo J. Math. Sci. 10, 228–247 (2016). https://doi.org/10.1007/s40863-015-0033-1

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