Left distributive left quasigroups

My PhD thesis is about left symmetric left quasigroups (also known as racks, quandles etc.) and their connection to other algebraic structures, such as groups and weakly associative loops. LDLQs are algebras with one binary operation such that all left translations are automorphisms. This can be axiomatized by

x*(y*z)=(x*y)*(x*z) for every x,y,z
the equation a*x=b has a unique solution for every a,b

The most natural example is a group with the operation of conjugation. There are some applications in knot theory, the knot quandle is a famous invariant of knot homotopy.

The thesis consists of the following chapters:

Introduction.
Preliminaries. Basic properties, normal forms for terms, definability, introduction to loops.
Left symmetric left distributive idempotent groupoids. (Or involutory quandles, or kei.) The main result is the correspondence of those of odd exponent to Bruck loops. Several structural results and some questions regarding cores of groups are presented. Not yet even close to publication.
On loops isotopic to left distributive quasigroups. The chapter contains a new solution of the eighth Belousov's problem: the smallest left distributive quasigroup which is not isotopic to any Bol loop. Just an observation.
Equational theory of group conjugation. This is a copy of the paper in Contributions to General Algebra 15, 177--185, Heyn, Klagenfurt, 2004. Download PDF here.
Subdirectly irreducible non-idempotent LDLQs. A much improved version will appear in Commun. Algebra in 2008. Download PDF here.
On varieties of left distributive left idempotent groupoids. This is a copy of the paper in Discussiones Math. - General Algebra and Appl. 24/2 (2004), 267--275. Download PDF here.
Appendix: Homomorphic images of subdirectly irreducible algebras. This is a slightly improved version of the paper in Comment. Math. Univ. Carolinae 42/3 (2001), 443--450.

For reading and reference, please use the research papers instead of the original text of the thesis - most of them were considerably improved. The thesis itself can be downloaded here and if you insist on reading it, don't forget to check the errata list.

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