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A loop is Osborn if it satisfies the identity x((yz)x) = (x λ \y)(zx). Is every Osborn loop universal, that is, is every isotope of an Osborn loop Osborn? If not, is there a nice identity characterizing universal Osborn loops? Proposed: by Michael Kinyon at Milehigh conference on quasigroups, loops, and nonassociative systems, Denver 2005
A loop that is both a left and right Bol loop is a Moufang loop. This is equivalent to any one of the following single Moufang identities holding for all x , y , z : x ∗ ( y ∗ ( x ∗ z )) = (( x ∗ y ) ∗ x ) ∗ z
A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. A strange loop hierarchy is "tangled" (Hofstadter refers to this as a "heterarchy"), in that there is no well defined highest or lowest level; moving through the levels, one eventually returns to the starting point, i.e., the original level.
In its most general form a loop group is a group of continuous mappings from a manifold M to a topological group G.. More specifically, [1] let M = S 1, the circle in the complex plane, and let LG denote the space of continuous maps S 1 → G, i.e.
In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same ...
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Loop modeling is a problem in protein structure prediction requiring the prediction of the conformations of loop regions in proteins with or without the use of a structural template. Computer programs that solve these problems have been used to research a broad range of scientific topics from ADP to breast cancer .
Similarly, a set of all smooth maps from S 1 to a Lie group G forms an infinite-dimensional Lie group (Lie group in the sense we can define functional derivatives over it) called the loop group. The Lie algebra of a loop group is the corresponding loop algebra.