Atabey Kaygun

The universal Hopf-cyclic theory

We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal category. Thus we unify all different types of Hopf cyclic (co)homologies under one single universal theory. We recover Hopf cyclic (co)homology of module algebras, comod- ule algebras and module coalgebras along with Hopf-Hochschild (co)homology of module algebras, and describe the missing theory for comodule coalgebras. Mathematics Subject Classification (2000). 16E40, 16W30, 46M18. Keywords. Hopf-cyclic cohomology, transpositive algebras, monads.

A temporal analysis of wealth in eighteenth-century Ottoman Kastamonu

This article studies temporal variations in wealth levels and distribution in an Ottoman context during the eighteenth century. By analysing the probate estate inventories of the Muslim deceased in Kastamonu, located in north-central Anatolia, we demonstrate that real wealth levels generally declined over the course of the century. Our analysis also suggests that the economic conditions of poor men, if not women, deteriorated more so than those of the rich, fuelling growing inequality. The article explores the factors that contributed to these trends and discusses the relevance of our findings for long-term economic development patterns in the region from a comparative perspective.

Quantum complex projective spaces from Toeplitz cubes

From N -tensor powers of the Toeplitz algebra, we construct a multi-pullback C*-algebra that is a noncommutative deformation of the complex projective space P.C/. Using Birkhoff’s Representation Theorem, we prove that the lattice of kernels of the canonical projections on components of the multi-pullback C*-algebra is free. This shows that our deformation preserves the freeness of the lattice of subsets generated by the affine covering of the complex projective space. Mathematics Subject Classification (2010). 06B10, 06B25.

Jacobi-Zariski exact sequence for Hochschild homology and cyclic (co)homology

We prove that for an inclusion of unital associative but not necessarily commutative kalgebras B ⊆A we have long exact sequences in Hochschild homology and cyclic (co)homology akin to the Jacobi-Zariski sequence in Andre-Quillen homology, provided that the quotient Bmodule A /B is flat. We also prove that for an arbitrary r-flat morphism φ : B → A with an H-unital kernel, one can express the Wodzicki excision sequence and our Jacobi-Zariski sequence in Hochschild homology and cyclic (co)homology as a single long exact sequence.

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

Hopf Modules and Noncommutative Differential Geometry

U_q(\mathfrak{g})

Spouse Selection and Marital Mobility in the Ottoman Empire: Observations from Eighteenth-Century Kastamonu

for an arbitrary semi-simple Lie algebra

Intergenerational mobility in the Ottoman Empire: Observations from eighteenth-century Kastamonu

\mathfrak{g}

A characteristic map for compact quantum groups

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

Hochschild cohomology of reduced incidence algebras

\mathfrak{g}