Some of my writings can be found online. Below is the list (later I will post here links to some errata and complimentary notes to some of the items). If other authors are not mentioned, the articles are authored just by me (Zoran Škoda). My thesis title was Coset spaces for quantum groups, and the abstract is at the link. For MR numbers see my MR numbers.
(Co)actions of Hopf algebras, actions of monoidal categories, localizations, descent, quotients
Localizations for construction of quantum coset spaces, in “Noncommutative geometry and Quantum groups”, W.Pusz, P.M. Hajac, eds. Banach Center Publications vol.61, pp. 265–298, Warszawa 2003, math.QA/0301090.
Coherent states for Hopf algebras, Letters in Mathematical Physics 81, N.1, pp. 1-17, July 2007. (earlier arXiv version: math.QA/0303357).
Noncommutative localization in noncommutative geometry, London Math. Society Lecture Note Series 330, ed. A. Ranicki; pp. 220–313, math.QA/0403276.
Distributive laws for actions of monoidal categories, math.CT/0406310.
Included-row exchange principle for quantum minors, math.QA/0510512.
Equivariant monads and equivariant lifts versus a 2-category of distributive laws, arXiv:0707.1609.
A simple algorithm for extending the identities for quantum minors to the multiparametric case, arXiv:0801.4965.
Bicategory of entwinings, arXiv:0805.4611.
Compatibility of (co)actions and localization, arXiv:0902.1398 (preliminary version).
Some equivariant constructions in noncommutative algebraic geometry, Georgian Mathematical Journal 16 (2009), No. 1, 183–202, arXiv:0811.4770; preprint MPIM2009-3.
Čech cocycles for quantum principal bundles, arxiv/1111.5316
Quantum bundles using coactions and localizations, in preparation.
There is also an ongoing project with Gabi Böhm on comonad compatible localization?s, comonadic machinery for gluing in equivariant setup and on globalizing Hopf-Galois extensions.
Some related entries to the tematics of this group of articles at the nlab are noncommutative geometry, equivariant noncommutative algebraic geometry, noncommutative scheme, quasicoherent sheaf, coherent sheaf, equivariant object. coring, comodule, localized coinvariant, distributive law, algebraic geometry, descent in noncommutative algebraic geometry, noncommutative algebraic geometry, bialgebra, Hopf algebra, Hopf action, Hopf module, comodule algebra, Hopf-Galois extension, quantum group, Ore set, Ore localization, matrix Hopf algebra, quantum Gauss decomposition, universal localization and in ‘private area’ of nlab also gluing categories from localizations, cleft extension of a space cover.
I introduced quantum heaps in Spring 2001, and they entered as a side-topic (Chapter 9 only) in my thesis. They were rediscovered by Grunspan in 2002 what spurred lots of activity and publications, but unfortunately nobody did refer nor use my work till the publication of my 2007 remake above.
Universal enveloping algebras and realizations via formal differential operators
N. Durov, S. Meljanac, A. Samsarov, Z. Škoda, A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra, Journal of Algebra 309, Issue 1, pp.318-359 (2007) math.RT/0604096, MPIM2006-62.
Twisted exterior derivative for enveloping algebras, arXiv:0806.0978.
S. Meljanac, Z. Škoda, Leibniz rules for enveloping algebras, pdf
S. Meljanac, D. Svrtan, Z. Škoda, Exponential formulas and Lie algebra type star products, Symmetry, Integrability and Geometry : Methods and Applications (SIGMA) 8 (2012) , 013; 1-15, arxiv/1006.0478
See also related entry symmetric ordering for Lie algebras. Recently, Meljanac and I have also exhibited a very beautiful Hopf algebroid structure on the noncommutative phase space with base coordinate space being a universal enveloping algebra; the article is close to be finished.
Higher stacks, categories and TQFT
H. Sati, U. Schreiber, Z. Škoda, D. Stevenson, Twisted nonabelian differential cohomology: Twisted (n-1)-brane n-bundles and their Chern-Simons (n+1)-bundles with characteristic (n+2)-classes, preliminary version, pdf.
Urs Schreiber, Z. Škoda, Categorified symmetries, 5th Summer School of Modern Mathematical Physics, SFIN, XXII Series A: Conferences, No A1, (2009), 397-424 (Editors: Branko Dragovich, Zoran Rakić). Extended 55 page version: arXiv/1004.2472 (the school/conference took place at the Institute of Physics, Belgrade, Serbia, July 6-17, 2008; SFIN is the abbreviation for series Sveske fizičkih nauka, ISSN 0354-9291).
With my student M. Bašić, I work on a programme of finding the integration objects for Leibniz algebras, which could be called Leibniz groups. Here is a manifesto:
Igor Sharygin and I started to write about unfinished research with tentative title Corrected coexponential map for universal enveloping of a Lie algebroid. We studied this subject at MPIM Bonn in Spring 2010, then a week at IHES in late November 2010 and talked much via skype in April and should continue these days.
In future, I would like to work closer to the BV-quantization program which is now being better geometrically understood.