Low dimensional cohomology of general conformal algebras $g{c}_N$

Abstract

We compute the low dimensional cohomologies ${\tilde{H}}^q(g{c}_N,C)$, $H^q(gc_N,\C)$ of the infinite rank general Lie conformal algebras $g{c}_N$ with trivial coefficients for $q\le 3,N=1$ or $q\le 2,N\ge 2$. We also prove that the cohomology of $g{c}_N$ with coefficients in its natural module is trivial, i.e., $H^*(gc_N,\C[\ptl]^N)=0$; thus partially solve an open problem of Bakalov-Kac-Voronov in [{\it Comm. Math. Phys.,} {\bf200} (1999), 561-598].

18 pages

Cited by in corpus (20)

• Loop Virasoro Lie Conformal Algebra
• 2-Cocycles of Original Deformative Schrödinger-Virasoro Algebras
• Loop Heisenberg-Virasoro Lie Conformal algebra
• Infinite rank Schrodinger-Virasoro type Lie conformal algebras
• Cohomology of Heisenberg-Virasoro conformal algebra
• Loop Schrödinger-Virasoro Lie conformal algebra
• A new class of Z-graded Lie conformal algebras of infinite rank
• Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $g{c}_1$
• Structures of $W(2,2)$ Lie conformal algebra
• A Lie conformal algebra of Block type
• Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type
• 2-Cocycles of the Lie superalgebras of Weyl type
• Simplicity of quadratic Lie conformal algebras
• Dual Lie bialgebra structures of the twisted Heisenberg-Virasoro type
• On a class of infinite simple Lie conformal algebras
• Structure of a class of Lie conformal algebras of Block type
• Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras
• Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules
• Loop W(a,b) Lie conformal algebra
• 2-Cocycles of Deformative Schrödinger-Virasoro Algebras