Results 11 to 20 of about 188 (47)
Applications of self-distributivity to Yang-Baxter operators and their cohomology
, 2018 Self-distributive (SD) structures form an important class of solutions to the Yang--Baxter equation, which underlie spectacular knot-theoretic applications of self-distributivity.
Lebed, Victoria
core +3 more sources
Quandle cohomology is a Quillen cohomology
, 2018 We show that the cohomology groups usually associated with racks and quandles agree with the Quillen cohomology groups for the algebraic theories of racks and quandles, respectively. We also explain how this makes available the entire range of tools that
Szymik, Markus
core +1 more source
Non-associative key establishment for left distributive systems
, 2013 We construct non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and other left distributive systems. Instantiations of these protocols using generalized shifted conjugacy in braid groups lead to instances of a ...
Kalka, Arkadius, Teicher, Mina
core +1 more source
Some simplicial complexes of universal Osborn loops
, 2014 A loop is shown to be a universal Osborn loop if and only if it has a particular simplicial complex. A loop is shown to be a universal Osborn loop and obeys two new identities if and only if it has another particular simplicial complex.
Jaiyeola, Temitope Gbolahan
core +2 more sources
Cohomology of finite monogenic self-distributive structures [PDF]
, 2015 A shelf is a set with a binary operation~$\op$ satisfying $a \op (b \op c) = (a \op b) \op (a \op c)$. Racks are shelves with invertible translations $b \mapsto a \op b$; many of their aspects, including cohomological, are better understood than those of
Lebed, Victoria
core +2 more sources
, 2018 We survey a few of the many results now known about the self-distributivity law and selfdistributive structures, with a special emphasis on the associated word problems and the algorithms solving them in good ...
Dehornoy, Patrick
core +1 more source
Iterated LD-Problem in non-associative key establishment [PDF]
, 2013 We construct new non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of these protocols relies on variations of the (simultaneous) iterated LD-problem and its generalizations. We
Kalka, Arkadius, Teicher, Mina
core
, 2005 Define an augmented LD-system, or ALD-system, to be a set equipped with two binary operations, one satisfying the left self-distributivity law $x * (y * z) = (x * y) * (x * z)$ and the other satisfying the mixed laws $(x o y) * z = x * (y * z)$ and $x * (
Dehornoy, Patrick
core +1 more source
Earth Resources Technology Satellite: Non-US standard catalog No. N-14 [PDF]
For abstract, see N74 ...
core +1 more source
Connected quandles and transitive groups
, 2015 We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and present new ...
Hulpke, Alexander +2 more
core