Frederick M. Goodman

Unbounded Derivations Tangential to Compact Groups of Automorphisms, II*

Let G be a compact abelian group, and τ an action of G on a C∗-algebra U, such that Uτ(γ)Uτ(γ)∗ = Uτ(0) Uτ for all γ ϵ G, where Uτ(γ) is the spectral subspace of U corresponding to the character γ on G. Derivations δ which are defined on the algebra UF of G-finite elements are considered. In the special case δ¦Uτ = 0 these derivations are characterized by a cocycle on G with values in the relative commutant of Uτ in the multiplier algebra of U, and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded. Under various restrictions on G and τ properties of the cocycle are deduced which again give characterizations of δ in terms of decompositions into generators of one-parameter subgroups of τ(G) and approximately inner derivations. Finally, a perturbation technique is devised to reduce the case δ(UF) ⊆ UF to the case δ(UF) ⊆ UF and δ¦Uτ = 0. This is used to show that any derivation δ with D(δ) = UF is wellbehaved and, if furthermore G = T1 and δ(UF) ⊆ UF the closure of δ generates a one-parameter group of ∗-automorphisms of U. In the case G = Td, d = 2, 3,… (finite), and δ(UF) ⊆ UF it is shown that δ extends to a generator of a group of ∗-automorphisms of the σ-weak closure of U in any G-covariant representation.

CYCLOTOMIC BIRMAN–WENZL–MURAKAMI ALGEBRAS, I: FREENESS AND REALIZATION AS TANGLE ALGEBRAS

The cyclotomic Birman–Wenzl–Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We show that the cyclotomic BMW algebras are free modules over any admissible, integral ground ring, and that they are isomorphic to cyclotomic versions of the Kauffman tangle algebras.

Lie algebras of unbounded derivations

Abstract In this paper some new results on analytic domination of operators and on integrability of Lie algebras of operators are proved and then our methods are applied to the study of Lie algebras of unbounded derivations in C ∗ algebras.

Unbounded derivations commuting with compact group actions

AbstractLet δ be a closed * derivation in aC* algebra

Closed derivations in commutative C∗ algebras

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Cellular Bases for Algebras with a Jones Basic Construction

which commutes with an ergodic action of a compact group on

Admissibility Conditions for Degenerate Cyclotomic BMW Algebras

\mathfrak{A}