Characters

Ambar N. Sengupta ()
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Ambar N. Sengupta: Louisiana State University, Department of Mathematics

Chapter Chapter 7 in Representing Finite Groups, 2012, pp 189-234 from Springer

Abstract: Abstract The character of a representation ρ of a group G on a finite-dimensional vector space E, over a field $$\mathbb{F}$$ , is the function χρ on G given by 7.1 $${\chi }_{\rho } : G \rightarrow\mathbb{F} : g\mapsto \mathrm{Tr}{\bigl (\rho (g)\bigr )}.$$ This logically sensible definition turns history on its head, because Frobenius [29] first constructed characters directly from groups, and certain associated determinants, and not from their representations.

Keywords: Irreducible Representation; Finite Group; Conjugacy Class; Regular Representation; Splitting Field (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-1231-1_7

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