Low dimensional cohomology of general conformal algebras $gc_N$

Details Low dimensional cohomology of general conformal algebras $gc_N$ Low dimensional cohomology of general conformal algebras $gc_N$

2004-02-26

arxiv.org/abs/math/0402421v1

J. Math. Phys., 45 (2004), 509--524

Mathematics

Quantum Algebra

18 pages

Scientific paper

We compute the low dimensional cohomologies $\tilde H^q(gc_N,C)$, $H^q(gc_N,\C)$ of the infinite rank general Lie conformal algebras $gc_N$ with trivial coefficients for $q\le3, N=1$ or $q\le2, N\ge2$. We also prove that the cohomology of $gc_N$ 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].

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