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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.
Loop recorded three Peel sessions for John Peel (11 August 1987, 14 June 1988 and 21 January 1990). A collection of these sessions entitled Wolf Flow was released in 1992. Following the split Loop's official studio albums were re-released on their Reactor label. Some of the records featured cover versions of Suicide, The Pop Group and Can tracks.
Comments: When the inner mapping group Inn(Q) is finite and abelian, then Q is nilpotent (Niemenaa and Kepka). The first question is therefore open only in the infinite case. Call loop Q of Csörgõ type if it is nilpotent of class at least 3, and Inn(Q) is abelian. No loop of Csörgõ type of nilpotency class higher than 3 is known.
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.
Loop (biochemistry), a flexible region in a protein's secondary structure; Loop (education), the process of advancing an elementary school teacher with his or her class; Loop (knot), one of the fundamental structures used to tie knots; Loop, the end of some dead-end streets; Loop, a type of fingerprint pattern
To be precise, the loop braid group on n loops is defined as the motion group of n disjoint circles embedded in a compact three-dimensional "box" diffeomorphic to the three-dimensional disk. A motion is a loop in the configuration space, which consists of all possible ways of embedding n circles into the 3-disk. This becomes a group in the same ...
The edge-path group E(X, v) is defined to be the set of edge-equivalence classes of edge-loops at v, with product and inverse defined by concatenation and reversal of edge-loops. The edge-path group is naturally isomorphic to π 1 (|X |, v), the fundamental group of the geometric realisation |X | of X. [24]
Loop Guru is a worldbeat group consisting of bassist/guitarist Salman Gita (born Sam Dodson) and programmer Jamuud (born David Muddyman). [1] They first met around 1980 and initially played together in The Transmitters and released their debut single as Loop Guru, "Shrine", in 1992.