Characters of Finite Abelian Groups
نویسنده
چکیده
Example 1.2. The trivial character of G is the homomorphism 1G defined by 1G(g) = 1 for all g ∈ G. Example 1.3. Let G be cyclic of order 4 with generator γ. Since γ4 = 1, a character χ of G has χ(γ)4 = 1, so χ takes only four possible values at γ, namely 1, −1, i, or −i. Once χ(γ) is known, the value of χ elsewhere is determined by multiplicativity: χ(γj) = χ(γ)j . So we get four characters, whose values can be placed in a table. See Table 1.
منابع مشابه
Representation theory of finite abelian groups
Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/01 finite abelian.pdf] 1. Simultaneous eigenvectors for finite abelian groups 2. Cancellation lemma, orthogonality of distinct characters 3. Representations of finite abelian groups 4. Fourier expansions on finite abelian groups 5. Appendix: spectral theor...
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