In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. For a Lie algebra g {\displaystyle {\mathfrak...

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible...

constructed: starting from a simple Lie algebra g {\displaystyle {\mathfrak {g}}} , one considers the loop algebra, L g {\displaystyle L{\mathfrak {g}}}...

algebra which is isomorphic with an untwisted affine Kac–Moody algebra. Using the centrally extended loop algebra one may construct a current algebra...

of a Hilbert space and associated operators reproducing the correct loop algebra) have been given by two groups (Lewandowski, Okołów, Sahlmann and Thiemann;...

0 with 1. The set of all loops in X forms a space called the loop space of X. Free loop Loop group Loop space Loop algebra Fundamental group Quasigroup...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

Mathematical Monographs. Oxford Science Publications, New York: Oxford University Press, ISBN 978-0-19-853535-5, MR 0900587 Loop space Loop algebra Quasigroup...

mounted as if it were a device LOOPS, the object system for Interlisp-D Loop (algebra), a quasigroup with an identity element Loop (graph theory), an edge that...

{Spin} (1,3)} . The Poincaré algebra is the Lie algebra of the Poincaré group. It is a Lie algebra extension of the Lie algebra of the Lorentz group. More...