In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. == Definition == For a Lie algebra g {\displaystyle {\mathfrak {g}}} over a field K {\displaystyle K} , if K [ t , t − 1 ] {\displaystyle K[t,t^{-1}]} is the space of Laurent polynomials, then L g := g ⊗ K [ t , t − 1 ] , {\displaystyle L{\mathfrak {g}}:={\mathfrak {g}}\otimes K[t,t^{-1}],} with the inherited bracket [ X ⊗ t m , Y ⊗ t n ] = [ X , Y ] ⊗ t m + n .
In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. == Definition == For a Lie algebra g {\displaystyle {\mathfrak {g}}} over a field K {\displaystyle K} , if K [ t , t − 1 ] {\displaystyle K[t,t^{-1}]} is the space of Laurent polynomials, then L g := g ⊗ K [ t , t − 1 ] , {\displaystyle L{\mathfrak {g}}:={\mathfrak {g}}\otimes K[t,t^{-1}],} with the inherited bracket [ X ⊗ t m , Y ⊗ t n ] = [ X , Y ] ⊗ t m + n .
Source: Wikipedia "Loop algebra" · CC BY-SA 4.0
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