Group Algebras

M. A. Naimark
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M. A. Naimark: Academy of Sciences, Steklov Institute of Mathematics

Chapter Chapter VI in Normed Algebras, 1972, pp 361-448 from Springer

Abstract: Abstract A set $$\mathfrak{G}$$ is called a group if there is defined a (generally non-commutative) product g1g2 of any two elements g1, g2 in $$\mathfrak{G}$$ , satisfying the following conditions: α) g1g2∈ $$\mathfrak{G}$$ for any two g1,g2∈ $$\mathfrak{G}$$ ; β) (g1g2)g3 = g1(g2g3) for any g1, g2, g3 ∈ $$\mathfrak{G}$$ ; γ) there exists a unique element e in $$\mathfrak{G}$$ such that eg = ge = g for all g ∈ $$\mathfrak{G}$$ ; e is called the identity element of the group $$\mathfrak{G}$$ ; δ) for every element g ∈ $$\mathfrak{G}$$ there exists a unique element in $$\mathfrak{G}$$ , which is denoted by g−1, such that gg−1 = g−1g = e; the element g−1 is called the inverse of g.

Keywords: Irreducible Representation; Invariant Measure; Compact Group; Maximal Ideal; Unitary Representation (search for similar items in EconPapers)
Date: 1972
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DOI: 10.1007/978-94-009-9260-3_6

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