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16 Jan 2024: γABA′B′ = φABεA′B′ ψA′B′εAB. for some symmetric spinors φ an ψ. ... for some complex Zα, α = 0, 1, 2, 3, where Z2 6= 0.

22 Jan 2024: 2 Background on quadratic formsWe collect together some standard definitions and results on quadratic forms. ... and henceto see that they satisfy some interesting symmetries (see Corollary 5.8).

31 Jan 2024: 223.4 The Galois correspondence. 25. 4 Some group theory 284.1 Free groups and presentations. ... H|{y0}[i/N,(i1)/N] : {y0} [iN ,. i1N ] X. lies entirely inside some Uα.

31 Jan 2024: If g2H = g′2H, then we know g. ′2 = g2 h for some h H. ... So we have to show p - ||. This is just some basic counting: we have. ||

29 Nov 2023: Thennecessarily ρ(0) = idV , and ρ(1) is some invertible linear map α on V. ... representation then ϕf,V = λ idV for some λ Cby Schur’s Lemma.

14 Sep 2023: By part (a),every such ν is the image of nΣX for some n. ... Y ||U|. as required. 2.2. Some stabilisers in G0 and their linear characters.

28 Nov 2023: It follows that every Banach algebra is isometricallyisomorphic to a closed subalgebra of B(X) for some Banach space X. ... B. Then. σB(x) σA(x) and σB(x) σA(x). It follows that σB(x) is the union of σA(x) together with some of the

14 Sep 2023: The em-phasis is on explicit formulae, some of which are taken from the existing literatureand some of which are new. ... 3A4A. 5A6 = λI4 for some scalar λ. Squaring both sides and using (9), (11) and (12) shows that λ2 = f66.

5 Jun 2024: For injectivity, let τ NFalg(A)n be a cyclesuch that ψ[τ] = 0, i.e., τ(n1,⟨0⟩) = b (1)n1b for some b A. ... By the firststep in the proof of Proposition 3.18, τW = τb+(1)dn b for some b Wh(M).

22 Aug 2023: Let us provide some motivation for both of these endeavours. Cubical small-cancellation as a means for producing examples. ... 2. N = G/K for some K < G,. 3. max{cd(G),2} cd(Γ) cd(G)1.