Differential calculi over quantum groups and twisted cyclic cocycles

By J. Kustermans, G. Murphy, L. Tuset. 2001

99 citations recorded by the source corpus.

Abstract We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the theory of twisted graded traces and their associated twisted cyclic cocycles. One of our principal results is a new method of constructing differential calculi, using twisted graded traces.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/49d8b5bc7ea682cb007ae033e47999e1aee601cb

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In Algebra and Number Theory

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Citations in the corpus

Braided cyclic cocycles and nonassociative geometry (2004, methodology): “Following the strategy in [7], we now define C(C;A, σ) = {φ ∈ HomC̄(A , 1) | φλ = φ} (3.”
Twisted homology of quantum SL(2) (2004, methodology): “In section 2 we recall how the twisted theory was discovered [9], then give the definitions of HH ∗ (A) and HC ∗ (A), and the underlying cyclic object.”
Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras (2006, methodology): “Let A be an algebra, and let σ be an algebra automorphism of A. The twisted Hochschild cohomology groups HH ∗ σ(A) of A with respect to σ were defined in [ KMT ] in a way exactly analogous to the twisted homology groups discussed in (3.1).”