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The logarithm of the derivative operator and higher spin algebras of $W\sb{\infty{}}$ type. (English) Zbl 0765.35049
Summary: The authors use the notion of the logarithm of the derivative operator to describe $W\sb \infty$ type algebras as central extensions of the algebra of differential operators. They also provide closed formulae for the truncations of $W\sb{1+\infty}$ to higher spin algebras with $s\geq M$, for all $M\geq 2$. The results are extended to matrix valued differential operators, introducing a logarithmic generalization of the Maurer-Cartan cocycle.

35Q53KdV-like (Korteweg-de Vries) equations
58J70Invariance and symmetry properties
81R10Infinite-dimensional groups and algebras motivated by physics
35S05General theory of pseudodifferential operators
17B68Virasoro and related algebras
Full Text: DOI
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