Representations of the Clifford Algebra 𝒞

In this chapter, we consider a suitable operator-theoretic representations of the Clifford algebra https://www.w3.org/1998/Math/MathML"> C = lim → ⁡   C k + 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781032637211/d7ba22f2-120e-401b-8c2f-40c3344e6436/content/unequ105-01.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> over the real field ℝ = 𝒞₀, because 𝒞 is a ℝ-Banach algebra. Such a representation is motivated by the CG C^∗ -probability space (M _𝒢, τ) of the CG algebra M _𝒢 of the Clifford group 𝒢, because the Clifford algebra 𝒞 is embedded in M _𝒢 .