Abelian and non-abelian second cohomologies of quantized enveloping algebras

By A. Masuoka. 2007

65 citations recorded by the source corpus.

Abstract For a class of pointed Hopf algebras including the quantized enveloping algebras, we discuss cleft extensions, cocycle deformations and the second cohomology. We present such a non-standard method of computing the abelian second cohomology that derives information from the non-abelian second cohomology classifying cleft extensions. As a sample computation, a quantum analogue of Whitehead's second lemma for Lie-algebra cohomology is proved.

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

View Paper: https://www.semanticscholar.org/paper/8f4f53ebeaadb67753a437ba019e6e2ffcfa8311

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Basic quasi-Hopf algebras over cyclic groups (2009, methodology): “liftings for coradically graded pointed Hopf algebras shall help us when we want to describe the category of representation of duals of pointed Hopf algebras. 10 IVAN EZEQUIEL ANGIONO´ Theorem 2.3.6 ([Ma]). Given a datum Dand families λ,µ, the Hopf algebra u(D,λ,µ) is a cocycle deformation of the as”
On finite dimensional Nichols algebras of diagonal type (2017, background): “By various reasons, we are also led to consider: • Pre-Nichols algebras of the braided vector space (V, c) [26,69]; these are graded connected Hopf algebras in HYD, say B = ⊕n∈N0B , with B1 V , that are 1 It is customary to omit c in the notation of the Nichols algebra.”