$w_{\infty }$ 3-algebra

Abstract

We use `lone-star' product of the $W_{\infty }$ generators as well as their commutation relations to obtain a $w_{\infty }$ 3-algebra by applying appropriate double scaling limits on the generators. We show explicitly that "Fundamental Identity Condition" (FI) of 3-algebra is satisfied.

9 pages, journal version

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• Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes
• Topological branes, p-algebras and generalized Nahm equations
• Classical and Quantal Ternary Algebras
• Hydrodynamics of N=6 Superconformal Chern-Simons Theories at Strong Coupling
• Super $w_{\infty }$ 3-algebra
• Infinite-dimensional 3-algebra and integrable system
• Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories
• On q-deformed infinite-dimensional n-algebra
• (p,q)-deformed Virasoro-Witt n-algebra
• 3-Algebraic structures of the quantum Calogero-Moser model