Serkan Sütlü

SAYD modules over Lie-Hopf algebras

In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.

Hopf-cyclic cohomology of quantum enveloping algebras

In this paper we calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra

Hamiltonian dynamics on matched pairs

U_q(\mathfrak{g})

Cyclic Homology and Quantum Orbits

for an arbitrary semi-simple Lie algebra

A characteristic map for compact quantum groups

\mathfrak{g}

Hochschild cohomology of reduced incidence algebras

with coefficients in a modular pair in involution. We show that its Hochschild cohomology is concentrated in a single degree determined by the rank of the Lie algebra

Characteristic classes of foliations via SAYD-twisted cocycles

\mathfrak{g}

A van Est Isomorphism for Bicrossed Product Hopf Algebras

.

Lagrangian dynamics on matched pairs

It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic two-form and canonical Poisson bracket are explicitly written. Various symplectic and Poisson reductions are perfomed. The Lie-Poisson bracket is derived. As an example, Lie-Poisson equations on

Topological Hopf algebras and their Hopf-cyclic cohomology

\mathfrak{sl}(2,\mathbb{C})^\ast