On anchored Lie algebras and the Connes–Moscovici bialgebroid construction
نویسندگان
چکیده
We show how the Connes–Moscovici bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras. As a supplement, we see these interact with study of flat bimodule connections.
منابع مشابه
the structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولLie $^*$-double derivations on Lie $C^*$-algebras
A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...
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• ei, fi. e1 = 1⊗ E1, e2 = 1⊗ E2; f1 = 1⊗ F1, f2 = 1⊗ F2. • e0, f0, h0. e0 = t⊗ [F1, F2] = t⊗ E31. f0 = t −1 ⊗ [E1, E2] = t−1 ⊗ E13. h0 = [e0, f0] = −1⊗ (H1 +H2) + c = −1⊗ (E11 + E33) + c • H. H = 1⊗H ⊕ Cc⊕ Cd. Note that c is just the central element c = h0 + h1 + h2. • Π. α1 = 1 = 2, α1(c) = α1(d) = 0 α2 = 1 = 2, α1(c) = α1(d) = 0 θ = α1 + α2 = 1 − 3, θ(c) = θ(d) = 0 δ : δ(1⊗H) = δ(c) = 0, δ(d...
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ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2022
ISSN: ['1661-6960', '1661-6952']
DOI: https://doi.org/10.4171/jncg/475